{"id":1198,"date":"2017-01-21T20:46:23","date_gmt":"2017-01-21T12:46:23","guid":{"rendered":"http:\/\/www.xuehelp.cn\/?p=1198"},"modified":"2017-01-21T20:46:23","modified_gmt":"2017-01-21T12:46:23","slug":"%e6%8e%92%e5%88%97%e7%bb%84%e5%90%88%e5%85%ac%e5%bc%8f","status":"publish","type":"post","link":"http:\/\/www.xuehelp.cn\/index.php\/archives\/1198","title":{"rendered":"\u6392\u5217\u7ec4\u5408\u516c\u5f0f"},"content":{"rendered":"<p>1\uff0e\u6392\u5217\u53ca\u8ba1\u7b97\u516c\u5f0f<\/p>\n<p>\u4ecen\u4e2a\u4e0d\u540c\u5143\u7d20\u4e2d\uff0c\u4efb\u53d6m(m\u2264n)\u4e2a\u5143\u7d20\u6309\u7167\u4e00\u5b9a\u7684\u987a\u5e8f\u6392\u6210\u4e00\u5217\uff0c\u53eb\u505a\u4ecen\u4e2a\u4e0d\u540c\u5143\u7d20\u4e2d\u53d6\u51fam\u4e2a\u5143\u7d20\u7684\u4e00\u4e2a\u6392\u5217\uff1b\u4ecen\u4e2a\u4e0d\u540c\u5143\u7d20\u4e2d\u53d6\u51fam(m\u2264n)\u4e2a\u5143\u7d20\u7684\u6240\u6709\u6392\u5217\u7684\u4e2a\u6570\uff0c\u53eb\u505a\u4ecen\u4e2a\u4e0d\u540c\u5143\u7d20\u4e2d\u53d6\u51fam\u4e2a\u5143\u7d20\u7684\u6392\u5217\u6570\uff0c\u7528\u7b26\u53f7 p(n,m)\u8868\u793a.<\/p>\n<p>p(n,m)=n(n-1)(n-2)\u2026\u2026(n-m+1)= n!\/(n-m)!(\u89c4\u5b9a0!=1).<!--more--><\/p>\n<p>2\uff0e\u7ec4\u5408\u53ca\u8ba1\u7b97\u516c\u5f0f<\/p>\n<p>\u4ecen\u4e2a\u4e0d\u540c\u5143\u7d20\u4e2d\uff0c\u4efb\u53d6m(m\u2264n)\u4e2a\u5143\u7d20\u5e76\u6210\u4e00\u7ec4\uff0c\u53eb\u505a\u4ecen\u4e2a\u4e0d\u540c\u5143\u7d20\u4e2d\u53d6\u51fam\u4e2a\u5143\u7d20\u7684\u4e00\u4e2a\u7ec4\u5408\uff1b\u4ecen\u4e2a\u4e0d\u540c\u5143\u7d20\u4e2d\u53d6\u51fam(m\u2264n)\u4e2a\u5143\u7d20\u7684\u6240\u6709\u7ec4\u5408\u7684\u4e2a\u6570\uff0c\u53eb\u505a\u4ecen\u4e2a\u4e0d\u540c\u5143\u7d20\u4e2d\u53d6\u51fam\u4e2a\u5143\u7d20\u7684\u7ec4\u5408\u6570.\u7528\u7b26\u53f7<\/p>\n<p>c(n,m) \u8868\u793a.<\/p>\n<p>c(n,m)=p(n,m)\/m!=n!\/((n-m)!*m!)\uff1bc(n,m)=c(n,n-m);<\/p>\n<p>3\uff0e\u5176\u4ed6\u6392\u5217\u4e0e\u7ec4\u5408\u516c\u5f0f<\/p>\n<p>\u4ecen\u4e2a\u5143\u7d20\u4e2d\u53d6\u51far\u4e2a\u5143\u7d20\u7684\u5faa\u73af\u6392\u5217\u6570\uff1dp(n,r)\/r=n!\/r(n-r)!.<\/p>\n<p>n\u4e2a\u5143\u7d20\u88ab\u5206\u6210k\u7c7b\uff0c\u6bcf\u7c7b\u7684\u4e2a\u6570\u5206\u522b\u662fn1,n2,&#8230;nk\u8fd9n\u4e2a\u5143\u7d20\u7684\u5168\u6392\u5217\u6570\u4e3a<\/p>\n<p>n!\/(n1!*n2!*&#8230;*nk!).<\/p>\n<p>k\u7c7b\u5143\u7d20,\u6bcf\u7c7b\u7684\u4e2a\u6570\u65e0\u9650,\u4ece\u4e2d\u53d6\u51fam\u4e2a\u5143\u7d20\u7684\u7ec4\u5408\u6570\u4e3ac(m+k-1,m).<br \/>\n\u6392\u5217\uff08Pnm(n\u4e3a\u4e0b\u6807\uff0cm\u4e3a\u4e0a\u6807)\uff09<\/p>\n<p>Pnm=n\u00d7\uff08n-1\uff09&#8230;.\uff08n-m+1\uff09\uff1bPnm=n\uff01\/\uff08n-m\uff09\uff01\uff08\u6ce8\uff1a\uff01\u662f\u9636\u4e58\u7b26\u53f7\uff09\uff1bPnn\uff08\u4e24\u4e2an\u5206\u522b\u4e3a\u4e0a\u6807\u548c\u4e0b\u6807\uff09 =n\uff01\uff1b0\uff01=1\uff1bPn1\uff08n\u4e3a\u4e0b\u68071\u4e3a\u4e0a\u6807\uff09=n<\/p>\n<p>\u7ec4\u5408\uff08Cnm(n\u4e3a\u4e0b\u6807\uff0cm\u4e3a\u4e0a\u6807)\uff09<\/p>\n<p>Cnm=Pnm\/Pmm \uff1bCnm=n\uff01\/m\uff01\uff08n-m\uff09\uff01\uff1bCnn\uff08\u4e24\u4e2an\u5206\u522b\u4e3a\u4e0a\u6807\u548c\u4e0b\u6807\uff09 =1 \uff1bCn1\uff08n\u4e3a\u4e0b\u68071\u4e3a\u4e0a\u6807\uff09=n\uff1bCnm=Cnn-m<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1\uff0e\u6392\u5217\u53ca\u8ba1\u7b97\u516c\u5f0f \u4ecen\u4e2a\u4e0d\u540c\u5143\u7d20\u4e2d\uff0c\u4efb\u53d6m(m\u2264n)\u4e2a\u5143\u7d20\u6309\u7167\u4e00\u5b9a\u7684\u987a\u5e8f\u6392\u6210\u4e00\u5217\uff0c\u53eb\u505a\u4ecen\u4e2a\u4e0d\u540c\u5143\u7d20\u4e2d\u53d6\u51fam [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[447],"_links":{"self":[{"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/posts\/1198"}],"collection":[{"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/comments?post=1198"}],"version-history":[{"count":1,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/posts\/1198\/revisions"}],"predecessor-version":[{"id":1199,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/posts\/1198\/revisions\/1199"}],"wp:attachment":[{"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/media?parent=1198"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/categories?post=1198"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/tags?post=1198"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}