{"id":61,"date":"2023-09-17T07:21:34","date_gmt":"2023-09-17T07:21:34","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%bb%84%e5%90%88%e6%95%b0%e4%ba%8c%e9%a1%b9%e5%bc%8f%e7%b3%bb%e6%95%b0%e6%80%a7%e8%b4%a8\/"},"modified":"2023-09-17T07:21:34","modified_gmt":"2023-09-17T07:21:34","slug":"%e7%bb%84%e5%90%88%e6%95%b0%e4%ba%8c%e9%a1%b9%e5%bc%8f%e7%b3%bb%e6%95%b0%e6%80%a7%e8%b4%a8","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%bb%84%e5%90%88%e6%95%b0%e4%ba%8c%e9%a1%b9%e5%bc%8f%e7%b3%bb%e6%95%b0%e6%80%a7%e8%b4%a8\/","title":{"rendered":"\u7ec4\u5408\u6570\uff08\u6216\u4e8c\u9879\u5f0f\u7cfb\u6570\uff09"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u7ec4\u5408\u6570\u4ee5\u53ca\u5b83\u7684\u8ba1\u7b97\u65b9\u5f0f\uff08\u516c\u5f0f\uff09\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5982\u4f55\u8ba1\u7b97\u4efb\u4f55\u7ec4\u5408\u6570\u7684\u793a\u4f8b\uff0c\u5e76\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002\u6211\u4eec\u8fd8\u5c55\u793a\u4e86\u7ec4\u5408\u6570\u7684\u6240\u6709\u5c5e\u6027\u548c\u5e94\u7528\u3002\u6700\u540e\uff0c\u6211\u4eec\u5b66\u4e60\u5982\u4f55\u76f4\u63a5\u4f7f\u7528\u8ba1\u7b97\u5668\u6c42\u7ec4\u5408\u6570\u7684\u7ed3\u679c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-numero-combinatorio\"><\/span>\u4ec0\u4e48\u662f\u7ec4\u5408\u6570\uff1f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\">\u5728\u6570\u5b66\u4e2d\uff0c<strong>\u7ec4\u5408\u6570<\/strong>\u4e5f\u79f0\u4e3a\u4e8c\u9879\u5f0f\u7cfb\u6570\uff0c\u662f\u7531 n \u4e2a\u5143\u7d20\uff08n&gt;k\uff09\u7ec4\u6210\u7684 k \u4e2a\u5143\u7d20\u7ec4\u7684\u666e\u901a\u7ec4\u5408\uff08\u4e0d\u91cd\u590d\u7684\u7ec4\u5408\uff09\u7684\u6570\u91cf\u3002<\/p>\n<p>\u7ec4\u5408\u6570\u5728\u62ec\u53f7\u4e2d\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-454ae3a63c42e51753f5b4cb18a4b4b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n \\\\ k \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"31\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u7ec4\u5408\u6570\u662f\u901a\u8fc7<em>k<\/em>\u8bfb\u53d6<em>\u7684<\/em>\u3002\u540c\u6837\uff0c <em>n<\/em>\u79f0\u4e3a\u5206\u5b50\uff0c <em>k<\/em>\u79f0\u4e3a\u9636\u3002<\/p>\n<p>\u4ec5\u51ed\u7ec4\u5408\u6570\u7684\u5b9a\u4e49\uff0c\u5f88\u96be\u7406\u89e3\u5176\u542b\u4e49\u3002\u7136\u800c\uff0c\u6211\u4eec\u73b0\u5728\u5c06\u4e86\u89e3\u5982\u4f55\u7528\u6570\u5b66\u65b9\u6cd5\u786e\u5b9a\u7ec4\u5408\u6570\uff0c\u7136\u540e\u6211\u4eec\u5c06\u66f4\u6df1\u5165\u5730\u7814\u7a76\u7ec4\u5408\u5b66\u7684\u6982\u5ff5\u3002\u4f60\u4f1a\u53d1\u73b0\u8fd9\u6837\u4f60\u4f1a\u66f4\u597d\u5730\u7406\u89e3\u5b83\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-del-numero-combinatorio\"><\/span>\u7ec4\u5408\u6570\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ec4\u5408\u6570\uff08\u6216\u4e8c\u9879\u5f0f\u7cfb\u6570\uff09\u503c\u7684\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-de-nombre-combinatoire.png\" alt=\"\u7ec4\u5408\u6570\u516c\u5f0f\" class=\"wp-image-1780\" width=\"184\" height=\"185\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u5728\u4ee3\u6570\u4e2d\uff0c\u611f\u53f9\u53f7\u5bf9\u5e94\u4e8e\u6570\u5b57\u7684\u9636\u4e58\u3002\u8981\u6c42\u4e00\u4e2a\u6570\u7684\u9636\u4e58\uff0c\u60a8\u9700\u8981\u5c06\u6240\u6709 1 \u7684\u6b63\u6574\u6570\u4e58\u4ee5\u8be5\u6570\u3002\u4f8b\u5982\uff0c\u8981\u8ba1\u7b97\u6570\u5b57 4 \u7684\u9636\u4e58\uff0c\u60a8\u5fc5\u987b\u5c06 1\u30012\u30013 \u548c 4 \u76f8\u4e58\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-092a0b9aa93c1211bc61b5b34844a3fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4! = 1\\cdot 2 \\cdot 3 \\cdot 4 =24\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"153\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e86\u89e3 0 \u7684\u9636\u4e58\u7b49\u4e8e 1 \u4e5f\u5f88\u91cd\u8981\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-255b29d39824041f4d334887daa9d55d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0! = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"45\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplo-de-como-calcular-un-numero-combinatorio\"><\/span>\u8ba1\u7b97\u7ec4\u5408\u6570\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u4ee5\u4e00\u6b65\u6b65\u786e\u5b9a\u7ec4\u5408\u6570\u7684\u503c\u4e3a\u4f8b\uff0c\u8ba9\u60a8\u770b\u770b\u5b83\u662f\u5982\u4f55\u5b8c\u6210\u7684\uff1a<\/p>\n<ul>\n<li>\u8ba1\u7b97\u7ec4\u5408\u6570 5 \u9664\u4ee5 3 \u7684\u503c\u3002<\/li>\n<\/ul>\n<p> 5 \u9664 3 \u7684\u4e8c\u9879\u5f0f\u7cfb\u6570\u5bf9\u5e94\u4e8e\u4ee5\u4e0b\u8868\u8fbe\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bdcbd05befcedad2d69b8388a30fa5ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}5 \\\\ 3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"29\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u5e94\u7528\u7ec4\u5408\u6570\u7684\u516c\u5f0f\uff0c\u4e3a\u4e86\u786e\u5b9a\u5176\u503c\uff0c\u6211\u4eec\u5fc5\u987b\u6267\u884c\u4ee5\u4e0b\u64cd\u4f5c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4d1d3925d89289554a4a5cea934b1e01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}5 \\\\ 3 \\end{pmatrix} = \\cfrac{5!}{3!(5-3)!}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"130\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6216\u540c\u7b49\u5b66\u5386\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9dccfbf9704a343dfff5e3b7999c3891_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}5 \\\\ 3 \\end{pmatrix} = \\cfrac{5!}{3!\\cdot 2!}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"99\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\u6211\u4eec\u627e\u5230\u9636\u4e58\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-00345c4e6c1e39974bfae029047f40de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}5 \\\\ 3 \\end{pmatrix} = \\cfrac{1\\cdot 2 \\cdot 3 \\cdot 4 \\cdot 5}{(1\\cdot 2 \\cdot 3) \\cdot (1\\cdot 2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"182\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4e58\u6cd5 1\u00b72\u00b73 \u5728\u5206\u5b50\u548c\u5206\u6bcd\u4e2d\u91cd\u590d\uff0c\u56e0\u6b64\u53ef\u4ee5\u901a\u8fc7\u6d88\u9664\u8fd9\u4e2a\u56e0\u5b50\u6765\u7b80\u5316\u5206\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-652f38c698238fcd311eb1d8c9367182_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}5 \\\\ 3 \\end{pmatrix} = \\cfrac{\\cancel{1\\cdot 2 \\cdot 3} \\cdot 4 \\cdot 5}{(\\cancel{1\\cdot 2 \\cdot 3)} \\cdot (1\\cdot 2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"182\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-454d692c958dbf69b0e1118f2f21982b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}5 \\\\ 3 \\end{pmatrix} = \\cfrac{ 4 \\cdot 5}{1\\cdot 2}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"89\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u8ba1\u7b97\u4e58\u79ef\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c8ac93ab4573c69daa96709c15dbb84d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}5 \\\\ 3 \\end{pmatrix} = \\cfrac{20}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"76\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u8fdb\u884c\u5212\u5206\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33b8f9d85113910811bd3491bd16f5a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}5 \\\\ 3 \\end{pmatrix} = \\bm{10}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"74\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Propiedades-del-numero-combinatorio\"><\/span>\u7ec4\u5408\u6570\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ec4\u5408\u6570\u6216\u4e8c\u9879\u5f0f\u7cfb\u6570\u53ef\u4ee5\u6839\u636e\u4ee5\u4e0b\u5c5e\u6027\u8fdb\u884c\u7ec4\u5408\uff1a<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u4e24\u4e2a<strong>\u4e92\u8865\u7ec4\u5408\u6570<\/strong>\u662f\u5177\u6709\u76f8\u540c\u5206\u5b50<em>n<\/em>\u4e14\u5176\u9636\u6570\u4e4b\u548c\u7b49\u4e8e\u8be5\u5206\u5b50n\u7684\u7ec4\u5408\u6570\u3002\u56e0\u6b64\uff0c\u4e24\u4e2a\u4e92\u8865\u7ec4\u5408\u6570\u7684\u7ed3\u679c\u662f\u76f8\u540c\u7684\u3002<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b8b93e5c1a92342922857dffd5ccbc61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n \\\\ k \\end{pmatrix} = \\begin{pmatrix}n \\\\ n-k \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"123\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u7ec4\u5408\u6570\u7684\u8fd9\u79cd\u7279\u6027\u4e5f\u79f0\u4e3a\u5bf9\u79f0\u6027\u3002<\/p>\n<p>\u4f8b\u5982\uff0c6 \u9664 4 \u7684\u7ed3\u679c\u4e0e 6 \u9664 2 \u7684\u7ed3\u679c\u76f8\u540c\uff0c\u56e0\u4e3a 6-4=2\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ad5997be8c69d9c99d4b72404feea1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}6 \\\\ 4 \\end{pmatrix} =\\cfrac{6!}{4!(6-4)!}  = \\cfrac{\\cancel{1\\cdot 2 \\cdot 3\\cdot 4}\\cdot 5 \\cdot 6}{(\\cancel{1\\cdot 2 \\cdot 3\\cdot 4})\\cdot (1\\cdot 2)}= \\cfrac{30}{2} = \\bm{15}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"384\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a30e46edb6ddcddccd5887cecd3d1c26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}6 \\\\ 2 \\end{pmatrix} =\\cfrac{6!}{2!(6-2)!} = \\cfrac{\\cancel{1\\cdot 2 \\cdot 3\\cdot 4}\\cdot 5 \\cdot 6}{(1\\cdot 2)\\cdot (\\cancel{1\\cdot 2 \\cdot 3\\cdot 4})}= \\cfrac{30}{2} = \\bm{15}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"384\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u5177\u6709\u76f8\u540c\u5206\u5b50\u548c\u987a\u5e8f\u7684\u4e24\u4e2a\u7ec4\u5408\u6570\u7684\u548c\u7b49\u4e8e\u53e6\u4e00\u4e2a\u7ec4\u5408\u6570\uff0c\u8be5\u7ec4\u5408\u6570\u7684\u5206\u5b50\u7b49\u4e8e\u52a0\u6cd5\u7684\u5206\u5b50\u52a01\uff0c\u5e76\u4e14\u5176\u9636\u5bf9\u5e94\u4e8e\u52a0\u6cd5\u7684\u9636\u6570\u4e2d\u7684\u6700\u5927\u503c\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u603b\u662f\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0d4265b42b3140a5bf8d8d8e6b74b925_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n\\\\ k \\end{pmatrix} + \\begin{pmatrix}n\\\\ k+1 \\end{pmatrix}= \\begin{pmatrix}n+1\\\\ k+1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"210\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-952934807b87f5983dc91ed1cdc3241a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}9\\\\ 2 \\end{pmatrix} + \\begin{pmatrix}9\\\\ 3 \\end{pmatrix}= \\begin{pmatrix}10\\\\ 3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"153\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u8be5\u6027\u8d28\u4e5f\u79f0\u4e3a\u5e15\u65af\u5361\u6cd5\u5219\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u8fd9\u4e2a\u516c\u5f0f\u4e5f\u53ef\u4ee5\u53cd\u5411\u5e94\u7528\uff0c\u5c06\u4e00\u4e2a\u7ec4\u5408\u6570\u5206\u89e3\u4e3a\u4e24\u4e2a\u66f4\u7b80\u5355\u7684\u7ec4\u5408\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-19cb7f9861c61d17e79fb65e0dfee9af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n\\\\ k \\end{pmatrix} = \\begin{pmatrix}n-1\\\\ k-1 \\end{pmatrix}+ \\begin{pmatrix}n-1\\\\ k \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"211\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0c\u7ec4\u5408\u6570 8 \u9664 4 \u7b49\u4e8e 7 \u9664 3 \u52a0 7 \u9664 4\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d6d42f8d7c9b4ba8dec3c27029b30f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}8\\\\ 4 \\end{pmatrix} = \\begin{pmatrix}7\\\\ 3 \\end{pmatrix}+ \\begin{pmatrix}7\\\\ 4 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"144\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u4efb\u4f55\u5927\u4e8e 1 \u7684\u6b63\u6570\u90fd\u7b49\u4e8e\u8be5\u6570\u672c\u8eab\u3002<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f50693630bdb11a333371c37fa023d5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n\\\\ 1 \\end{pmatrix} =n\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"68\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u8be5\u5c5e\u6027\u7684\u539f\u56e0\u662f\u4e00\u4e2a\u6570\u5b57\u7684\u9636\u4e58\u7b49\u4e8e\u524d\u4e00\u4e2a\u6570\u5b57\u7684\u9636\u4e58\u4e58\u4ee5\u8be5\u6570\u5b57\u672c\u8eab\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-538fd046daf5726856948bbed0bc1b2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n \\\\ 1 \\end{pmatrix} =\\cfrac{n!}{1!(n-1)!} = \\cfrac{n\\cdot (n-1) \\cdot (n-2)\\cdots 1}{(n-1) \\cdot (n-2)\\cdots 1}= n\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"375\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6b64\u7c7b\u7ec4\u5408\u6570\u7684\u793a\u4f8b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-48a62f11350db57d4ffc7cc3b4169a4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}12\\\\ 1 \\end{pmatrix} =12 \\qquad  \\begin{pmatrix}5\\\\ 1 \\end{pmatrix} =5  \\qquad \\begin{pmatrix}9\\\\ 1 \\end{pmatrix} =9\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"294\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u4efb\u4f55\u5927\u4e8e 0 \u7684\u6b63\u6570\u90fd\u7b49\u4e8e 1\u3002<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-00194e1abf490a12e203ed5e8797c7f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n\\\\ 0 \\end{pmatrix} =1\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"65\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u6837\u7684\u7ec4\u5408\u6570\u7684\u5206\u6570\u7684\u5206\u6bcd\u5c06\u59cb\u7ec8\u7b49\u4e8e\u5206\u6570\u7684\u5206\u5b50\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ffcbe8b8aab8ef3a6a6288df9fcd9147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n\\\\ 0 \\end{pmatrix} =\\cfrac{n!}{0!(n-0)!} =\\cfrac{n!}{n!} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"206\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u7ec4\u5408\u6570\u7684\u4f8b\u5b50\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-37cec31b317b48dc0080810360941f4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}6\\\\ 0 \\end{pmatrix} =1 \\qquad  \\begin{pmatrix}2\\\\ 0 \\end{pmatrix} =1 \\qquad  \\begin{pmatrix}23\\\\ 0 \\end{pmatrix} =1\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"284\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u6bcf\u4e2a\u6570\u5b57\u672c\u8eab\u90fd\u7b49\u4e8e 1\u3002<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1eb1cfb501b54a435a581adc68c2f2f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n\\\\ n \\end{pmatrix} =1\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"65\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u8fd9\u662f\u6f14\u793a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5ce41f441169a0f1098f900d74b03b38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n\\\\ n \\end{pmatrix} =\\cfrac{n!}{n!(n-n)!} =\\cfrac{n!}{n!\\cdot 0!}= \\cfrac{n!}{n!} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"277\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u7ec4\u5408\u6570\u7684\u4f8b\u5b50\u5982\u4e0b\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-341fc99ef910038cf53561a9b6680f70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}5\\\\ 5 \\end{pmatrix} =1 \\qquad  \\begin{pmatrix}37\\\\ 37 \\end{pmatrix} =1 \\qquad  \\begin{pmatrix}14\\\\ 14 \\end{pmatrix} =1\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"293\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Como-calcular-un-numero-combinatorio-con-la-calculadora\"><\/span>\u5982\u4f55\u7528\u8ba1\u7b97\u5668\u8ba1\u7b97\u7ec4\u5408\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u5df2\u7ecf\u4e86\u89e3\u4e86\u5982\u4f55\u627e\u5230\u6216\u591a\u6216\u5c11\u7b80\u5355\u6570\u5b57\u7684\u7ec4\u5408\u6570\uff0c\u4f46\u662f\u5f53\u6211\u4eec\u5fc5\u987b\u5904\u7406\u975e\u5e38\u5927\u7684\u6570\u91cf\u65f6\uff0c\u6700\u597d\u4f7f\u7528\u8ba1\u7b97\u5668\u6765\u786e\u5b9a\u7ec4\u5408\u6570\u3002\u73b0\u5728\u6211\u4eec\u5c06\u4e86\u89e3\u5982\u4f55\u5728\u8ba1\u7b97\u5668\u4e2d\u8f93\u5165\u7ec4\u5408\u6570\u5b57\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u7528\u8ba1\u7b97\u5668\u8ba1\u7b97\u7ec4\u5408\u6570\u7684\u952e\u662f<strong>nCr \u952e<\/strong>\u3002\u800c\u8981\u786e\u5b9a\u7ec4\u5408\u6570\u7684\u503c\uff0c\u5fc5\u987b\u5148\u8f93\u5165\u7ec4\u5408\u6570\u7684\u5206\u5b50\uff0c\u5176\u6b21\u6309nCr\u952e\uff0c\u7136\u540e\u8f93\u5165\u7ec4\u5408\u6570\u7684\u987a\u5e8f\uff0c\u6700\u540e\u6309\u7b49\u4e8e\u952e\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c0415dd33a2b02d34f25b3ce7ed9eb5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n\\\\ k \\end{pmatrix}\\quad \\color{red}\\bm{\\longrightarrow} \\quad \\color{black} n \\rightarrow \\boxed{nCr} \\rightarrow k \\rightarrow \\boxed{=}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"339\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5728 CASIO \u79d1\u5b66\u8ba1\u7b97\u5668\u4e0a\uff0cnCr \u952e\u901a\u5e38\u6709\u81ea\u5df1\u7684\u6309\u94ae\u6216\u4f4d\u4e8e\u9664\u6cd5\u6309\u94ae\u4e0a\u65b9\uff0c\u5177\u4f53\u53d6\u51b3\u4e8e\u578b\u53f7\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u60f3\u77e5\u9053 10 \u9664\u4ee5 6 \u7684\u7ec4\u5408\u6570\u662f\u591a\u5c11\uff0c\u6211\u4eec\u5fc5\u987b\u6267\u884c\u4ee5\u4e0b\u5e8f\u5217\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2644b485893664160985bcfdbea173c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}10\\\\ 6 \\end{pmatrix}\\quad \\color{red}\\bm{\\longrightarrow} \\quad \\color{black} 10 \\rightarrow \\boxed{nCr} \\rightarrow 6 \\rightarrow \\boxed{=} \\rightarrow 210\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"407\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Aplicaciones-del-numero-combinatorio\"><\/span>\u7ec4\u5408\u6570\u7684\u5e94\u7528<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5982\u679c\u60a8\u5df2\u7ecf\u505a\u5230\u4e86\u8fd9\u4e00\u70b9\uff0c\u60a8\u53ef\u80fd\u5df2\u7ecf\u77e5\u9053\u5982\u4f55\u89e3\u51b3\u4efb\u4f55\u7ec4\u5408\u6570\uff0c\u5b8c\u7f8e\u3002\u4f46\u662f\u2026\u2026\u7ec4\u5408\u6570\u6709\u4ec0\u4e48\u7528\u5462\uff1f\u597d\u5427\uff0c\u90a3\u4e48\u6211\u4eec\u5c06\u770b\u5230\u8fd9\u79cd\u975e\u5e38\u7279\u6b8a\u7684\u64cd\u4f5c\u6240\u5e26\u6765\u7684\u6240\u6709\u4f18\u70b9\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Combinatoria\"><\/span>\u7ec4\u5408\u5b66<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u9875\u9762\u9876\u90e8\u770b\u5230\u7684\uff0c\u7ec4\u5408\u6570\u7684\u7ed3\u679c<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-72853e95c6b133307a284ae9da39d7d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n\\\\ k \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"31\" style=\"vertical-align: -17px;\"><\/p>\n<p>\u8868\u793a\u53ef\u80fd\u7684\u7ec4\u6570<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u53ef\u4ee5\u7531\u4e00\u7ec4\u603b\u5171\u6784\u6210\u7684\u5143\u7d20<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u9879\u76ee\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u4e00\u4e9b\u7ec4\u5408\u95ee\u9898\u53ef\u4ee5\u4f7f\u7528\u7ec4\u5408\u6570\uff08\u6216\u4e8c\u9879\u5f0f\u7cfb\u6570\uff09\u6765\u89e3\u51b3\u3002\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5982\u4f55\u505a\u5230\u8fd9\u4e00\u70b9\uff1a<\/p>\n<ul>\n<li>\u5728\u4e00\u4e2a 30 \u540d\u5b66\u751f\u7684\u73ed\u7ea7\u4e2d\uff0c\u6211\u4eec\u60f3\u8981\u9009\u62e9\u4e00\u7ec4 4 \u540d\u5b66\u751f\u6765\u6267\u884c\u67d0\u4e9b\u4efb\u52a1\u3002\u603b\u5171\u53ef\u4ee5\u7ec4\u6210\u591a\u5c11\u4e2a\u4e0d\u540c\u7684\u7ec4\uff1f<\/li>\n<\/ul>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5b66\u751f\u7684\u987a\u5e8f\u5e76\u4e0d\u91cd\u8981\uff0c\u540c\u4e00\u5b66\u751f\u4e0d\u4f1a\u5728\u7ec4\u5185\u91cd\u590d\u4e24\u6b21\uff0c\u5e76\u4e14\u5e76\u975e\u6240\u6709\u5b66\u751f\u90fd\u8fdb\u5165\u8be5\u7ec4\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u5229\u7528\u7ec4\u5408\u6570\u516c\u5f0f\u6765\u786e\u5b9a\u8be5\u7fa4\u53ef\u4ee5\u6709\u591a\u5c11\u79cd\u5f62\u6210\u65b9\u5f0f\u3002<\/p>\n<p>\u4e3a\u6b64\uff0c\u60a8\u5fc5\u987b\u4ee5\u5b66\u751f\u603b\u6570\u4e3a\u5206\u5b50\uff0c\u4ee5\u7ec4\u6210\u5c0f\u7ec4\u7684\u5b66\u751f\u4eba\u6570\u4e3a\u987a\u5e8f\u8ba1\u7b97\u7ec4\u5408\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-11eac1a8918444a100bca85bfbd6e701_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}30 \\\\ 4 \\end{pmatrix} =\\cfrac{30!}{4!(30-4)!} =\\cfrac{30\\cdot 29 \\cdot 28 \\cdot 27 \\cdot \\cancel{26!}}{4\\cdot 3 \\cdot 2 \\cdot 1 \\cdot \\cancel{26!}} = \\cfrac{657720}{24}=\\bm{27405}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"464\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u53ef\u80fd\u7684\u7ec4\u5408\u603b\u6570\u4e3a 27,405 \u7ec4\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Binomio-de-Newton\"><\/span>\u725b\u987f\u4e8c\u9879\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u7ec4\u5408\u6570\u7684\u53e6\u4e00\u4e2a\u5e94\u7528\u662f\u725b\u987f\u4e8c\u9879\u5f0f\u3002\u725b\u987f\u4e8c\u9879\u5f0f\u662f\u7531\u4e24\u9879\u4e00\u8d77\u6c42\u6210\u6574\u6570\u7684\u591a\u9879\u5f0f\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u725b\u987f\u4e8c\u9879\u5f0f\u662f\u54cd\u5e94\u4ee5\u4e0b\u4ee3\u6570\u8868\u8fbe\u5f0f\u7684\u591a\u9879\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7cb070eb92ff2ce3199cbbf72ab6122_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^n\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u663e\u7136\uff0c\u5982\u679c\u4e8c\u9879\u5f0f\u662f\u5e73\u65b9\u7684\uff0c\u5219\u610f\u5473\u7740\u5b83\u662f<strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6052\u7b49\u5f0f\u4ea7\u54c1-\u663e\u7740\u7684\u7b49\u5f0f\u89e3\u51b3\u7ec3\u4e60\/\">\u663e\u7740\u7684\u6052\u7b49\u5f0f<\/a><\/span><\/strong>\uff0c\u56e0\u6b64\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u7528\u76f8\u5e94\u7684\u516c\u5f0f\u8fdb\u884c\u8ba1\u7b97\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5f53\u4e8c\u9879\u5f0f\u589e\u5927\u5230\u5f88\u5927\u7684\u6570\u65f6\uff0c\u8ba1\u7b97\u5c31\u53d8\u5f97\u76f8\u5f53\u56f0\u96be\u3002\u725b\u987f\u4e8c\u9879\u5f0f\u5b9a\u7406\u8868\u660e\uff0c\u8fd9\u4e9b\u7c7b\u578b\u7684\u591a\u9879\u5f0f\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u4ece\u7ec4\u5408\u6570\u8ba1\u7b97\u51fa\u6765\u3002<\/p>\n<p>\u5355\u51fb\u4ee5\u4e0b\u94fe\u63a5\uff0c\u4e86\u89e3<strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u4e8c\u9879\u5f0f\u6216\u725b\u987f\u4e8c\u9879\u5f0f\u5b9a\u7406\u516c\u5f0f\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\/\">\u725b\u987f\u4e8c\u9879\u5f0f\u516c\u5f0f<\/a><\/span><\/strong>\u662f\u4ec0\u4e48\u53ca\u5176\u8ba1\u7b97\u65b9\u6cd5\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u793a\u4f8b\u5e76\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002\u6700\u540e\uff0c\u60a8\u5c06\u53d1\u73b0\u8fd9\u4e2a\u5b9a\u7406\u7684\u5947\u5999\u5386\u53f2\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Triangulo-de-Tartaglia-o-de-Pascal\"><\/span>\u5854\u5854\u5229\u4e9a\uff08\u6216\u5e15\u65af\u5361\uff09\u4e09\u89d2\u5f62<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u6b63\u5982\u60a8\u5728\u672c\u6587\u4e2d\u6240\u770b\u5230\u7684\uff0c\u624b\u52a8\u8ba1\u7b97\u5927\u6570\u7684\u4e8c\u9879\u5f0f\u7cfb\u6570\u53ef\u80fd\u65e2\u8d39\u529b\u53c8\u590d\u6742\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u4f7f\u7528\u5854\u5854\u5229\u4e9a\u4e09\u89d2\u5f62\uff08\u4e5f\u79f0\u4e3a\u5e15\u65af\u5361\u4e09\u89d2\u5f62\uff09\uff0c\u53ef\u4ee5\u4f7f\u7528\u52a9\u8bb0\u7b26\u89c4\u5219\u8f7b\u677e\u786e\u5b9a\u6240\u6709\u7ec4\u5408\u6570\u3002\u8fd9\u5728\u903b\u8f91\u4e0a\u975e\u5e38\u6709\u7528\uff0c\u56e0\u4e3a\u5b83\u5728\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u8282\u7701\u4e86\u5927\u91cf\u65f6\u95f4\u3002<\/p>\n<p>\u8981\u786e\u5207\u4e86\u89e3\u5982\u4f55\u6267\u884c\u6b64\u64cd\u4f5c\uff0c\u8bf7\u53c2\u9605<a href=\"https:\/\/mathority.org\/cn\/\u5854\u5854\u5229\u4e9a\u6216\u5e15\u65af\u5361\u4e09\u89d2\u5f62\/\"><strong><span style=\"text-decoration: underline;\">\u5854\u5c14\u5854\u5229\u4e9a\u7684\u4e09\u89d2\u5f62<\/span><\/strong><\/a>\u89e3\u91ca\u3002\u5728\u6b64\u94fe\u63a5\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u8fd9\u4e2a\u795e\u79d8\u7684\u4e09\u89d2\u5f62\u662f\u4ec0\u4e48\u3001\u5b83\u7684\u7528\u9014\u662f\u4ec0\u4e48\uff08\u5b83\u6709\u4ee4\u4eba\u60ca\u8bb6\u7684\u5e94\u7528\uff09\ud83d\ude2e\u4ee5\u53ca\u5b83\u7684\u8d77\u6e90\u662f\u4ec0\u4e48\uff08\u5b83\u5df2\u7ecf\u5728 1000 \u591a\u5e74\u524d\u88ab\u4f7f\u7528\uff09\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-numeros-combinatorios\"><\/span>\u89e3\u51b3\u4e86\u7ec4\u5408\u6570\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u8ba9\u60a8\u80fd\u591f\u7ec3\u4e60\u5e76\u5145\u5206\u7406\u89e3\u6240\u89e3\u91ca\u7684\u6982\u5ff5\uff0c\u6211\u4eec\u4e3a\u60a8\u63d0\u4f9b\u4e86\u51e0\u4e2a\u9010\u6b65\u89e3\u51b3\u7ec4\u5408\u6570\u7684\u7ec3\u4e60\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u627e\u51fa 9 \u00d7 5 \u7684\u7ec4\u5408\u6570\uff08\u4e0d\u4f7f\u7528\u8ba1\u7b97\u5668\uff09\u3002 <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u627e\u5230 5 \u4e2a\u7ec4\u5408\u6570\u4e2d\u7684 9 \u4e2a\u7684\u503c\uff0c\u6211\u4eec\u53ea\u9700\u5e94\u7528\u9636\u4e58\u516c\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e2bb8cd51adb05d2cbc2299f179ed44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}9 \\\\ 5 \\end{pmatrix} =\\cfrac{9!}{5!(9-5)!} = \\cfrac{9\\cdot 8 \\cdot 7\\cdot 6\\cdot \\cancel{5!}}{\\cancel{5!} \\cdot (4 \\cdot 3 \\cdot 2 \\cdot 1)}= \\cfrac{3024}{24} = \\bm{126}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"381\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u4e0b\u9762\u4e24\u4e2a\u7ec4\u5408\u6570\u76f8\u52a0\u7684\u7ed3\u679c\u662f\u4ec0\u4e48\uff1f \uff08\u4e0d\u5e26\u8ba1\u7b97\u5668\uff09 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32e3c53635693ea4e1648d7d0a12288c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}10\\\\ 6 \\end{pmatrix} + \\begin{pmatrix}10\\\\ 7 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"103\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u6839\u636e\u7ec4\u5408\u6570\u7684\u6027\u8d28\uff0c\u95ee\u9898\u7684\u603b\u548c\u7b49\u4e8e\u4ee5\u4e0b\u7ec4\u5408\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-22963c45606c26da0bcb662a5534f1b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}10\\\\ 6 \\end{pmatrix} + \\begin{pmatrix}10\\\\ 7 \\end{pmatrix}=\\begin{pmatrix}11\\\\ 7 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"171\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u8ba1\u7b97 7 \u4e2d\u7684\u7ec4\u5408\u6570 11 \u5c31\u8db3\u591f\u4e86\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d56c6d97bd8761d053d98039fc064652_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}11 \\\\ 7 \\end{pmatrix} =\\cfrac{11!}{7!(11-7)!} = \\cfrac{11\\cdot 10 \\cdot 9\\cdot 8 \\cdot \\cancel{7!}}{\\cancel{7!} \\cdot (4 \\cdot 3 \\cdot 2 \\cdot 1)}= \\cfrac{7920}{24} = \\bm{330}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"403\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u5224\u65ad\u4e0b\u5217\u7ec4\u5408\u6570\u662f\u5426\u76f8\u7b49\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-be04129d96ae292a529d8bd986bc31f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}6\\\\ 0 \\end{pmatrix} \\qquad  \\begin{pmatrix}6\\\\ 1 \\end{pmatrix}\\qquad  \\begin{pmatrix}6\\\\ 6 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"176\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u627e\u5230\u4e09\u4e2a\u7ec4\u5408\u6570\u7684\u7ed3\u679c\uff0c\u60a8\u4e0d\u9700\u8981\u4f7f\u7528\u8ba1\u7b97\u5668\uff0c\u4f46\u7531\u4e8e\u7ec4\u5408\u6570\u7684\u6027\u8d28\uff0c\u5b83\u4eec\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u627e\u5230\u3002<\/p>\n<p class=\"has-text-align-left\">\u9996\u5148\uff0c\u4efb\u610f\u5927\u4e8e0\u7684\u6570\u7684\u7ec4\u5408\u6570\u90fd\u662f1\u3002\u56e0\u6b64\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fda7c6f2f56556c6af74bde199613037_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}6\\\\ 0 \\end{pmatrix} =1\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"64\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u4efb\u4f55\u5927\u4e8e\u4e00\u7684\u6570\u5b57\u90fd\u7b49\u4e8e\u8be5\u6570\u5b57\u672c\u8eab\u3002\u7136\u800c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e60628beab23d09954027294de2fabf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}6\\\\ 1 \\end{pmatrix} =6\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"65\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u4efb\u4f55\u7531\u76f8\u540c\u6570\u5b57\u91cd\u590d\u4e24\u6b21\u5f62\u6210\u7684\u7ec4\u5408\u6570\u90fd\u7b49\u4e8e 1\u3002\u6240\u4ee5\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-659cabb0351db5bf4148f2b2c0f536f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}6\\\\ 6 \\end{pmatrix} =1\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"64\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7efc\u4e0a\u6240\u8ff0\uff0c\u95ee\u9898\u4e2d\u7684\u7b2c\u4e00\u4e2a\u548c\u7b2c\u4e09\u4e2a\u7ec4\u5408\u6570\u76f8\u7b49\uff0c\u4f46\u4e0e\u4e2d\u95f4\u7684\u7ec4\u5408\u6570\u4e0d\u540c\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-18528223523fe6672b927769a53ef7ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}6\\\\ 0 \\end{pmatrix}= \\begin{pmatrix}6\\\\ 6 \\end{pmatrix}\\neq \\begin{pmatrix}6\\\\ 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"146\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u7ec4\u5408\u6570\u4ee5\u53ca\u5b83\u7684\u8ba1\u7b97\u65b9\u5f0f\uff08\u516c\u5f0f\uff09\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5982\u4f55\u8ba1\u7b97\u4efb\u4f55\u7ec4\u5408\u6570\u7684\u793a\u4f8b\uff0c\u5e76\u901a\u8fc7\u9010 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e7%bb%84%e5%90%88%e6%95%b0%e4%ba%8c%e9%a1%b9%e5%bc%8f%e7%b3%bb%e6%95%b0%e6%80%a7%e8%b4%a8\/\"> <span class=\"screen-reader-text\">\u7ec4\u5408\u6570\uff08\u6216\u4e8c\u9879\u5f0f\u7cfb\u6570\uff09<\/span> \u67e5\u770b\u5168\u6587 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