求教高中数学n个元素全错排的公式是什么?感谢!!! 错排公式的介绍
\u9519\u6392\u516c\u5f0f\uff0c\u8bb2\u89e3\u4e00\u6392\u4e5d\u4e2a\u5750\u4f4d\u6709\u516d\u4e2a\u4eba\u5750\uff0c\u82e5\u6bcf\u4e2a\u7a7a\u4f4d\u4e24\u8fb9\u90fd\u5750\u6709\u4eba\uff0c
\u5148\u5750\u4eba\uff0c\u5171\u67096\uff01=720\u79cd
\u518d\u5728\u4efb\u610f2\u4eba\u7684\u4e2d\u95f4\u6216\u662f\u5de6\u53f3\u7aef\u70b9\u5171\u63d2\u51653\u4e2a\u7a7a\u4f4d\uff0c\u67097\u4e2a\u4f4d\u7f6e\u53ef\u653e\u7a7a\u4f4d\u3002\u6240\u4ee5\u7a7a\u4f4d\u63d2\u6cd5\u4e3aC(7,3)=35\u79cd\u3002
\u5171\u670935*720=25200\u79cd\u65b9\u6848\u3002
\u7f16\u53f7\u4e3a1\uff0c2\uff0c3\uff0c4\uff0c5\u7684\u4e94\u4e2a\u4eba\uff0c\u5206\u522b\u5750\u5728\u7f16\u53f7\u4e3a1\uff0c2\uff0c3\uff0c4\uff0c5\u7684\u5ea7\u4f4d\u4e0a\uff0c
\u9519\u6392\u6570\u7684\u8ba1\u7b97\u516c\u5f0f\u4e3aD(n)=(n-1)*(D(n-1)+D(n-2)\uff0c\u4e14D(1)=0,D(2)=1,D(3)=2,D(4)=9
\u5168\u9519\u7684\u5750\u6cd5\u6709D(5)=4*(2+9)=44\u79cd
\u53ea\u6709\u4e00\u4eba\u5750\u5bf9\u53f7\u7801\u7684\u67095*D(4)=5*9=45\u79cd
\u53ea\u6709\u4e8c\u4eba\u5750\u5bf9\u53f7\u7801\u7684\u6709C(5,2)*D(3)=10*2=20\u79cd
\u5219\u81f3\u591a\u6709\u4e24\u4e2a\u53f7\u7801\u4e00\u81f4\u7684\u5750\u6cd5\u79cd\u6570\u4e3a44+45+20=109\u79cd
\u5173\u4e8e\u9519\u6392\u7684\u95ee\u9898\uff0c\u8be6\u89c1\uff1ahttp://baike.baidu.com/view/668994.htm
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L(2)=1
L(3)=2
L(4)=L(3)*C(3,1)+L(2)*C（3,1）=9
......
L(n+1)=L(n)*C(n,1)+L(n-1)*C(n,1)
.....
Dn=n!(1-1/1！+1/2！-1/3!+...+(-1)^n*1/n!)
=n!*[1-1/(1!)+1/(2!)-1/(3!)+1/(4!)+...+(-1)^n/(n!)]
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绛旓細涓涓厓绱犵殑閿欐帓涓0涓備袱涓厓绱犵殑閿欐帓涓1涓紝涓変釜鍏冪礌鐨勯敊鎺掍负2涓紝鍥涗釜鍏冪礌鐨勯敊鎺掍负9锛屼簲涓厓绱犵殑閿欐帓涓44銆傞敊鎺掑叿鏈夌畝鍗曠殑璁＄畻鍏紡锛欴(n) = (n-1) [D(n-2) + D(n-1)]璁＄畻杩囩▼濡備笅锛欴锛1锛=0D锛2锛=1D锛3锛=2锛0+1锛=2D锛4锛=3锛2+1锛=9D锛5锛=4锛9+2锛=44 ...
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绛旓細涓涓厓绱犵殑閿欐帓涓0涓備袱涓厓绱犵殑閿欐帓涓1涓紝涓変釜鍏冪礌鐨勯敊鎺掍负2涓紝鍥涗釜鍏冪礌鐨勯敊鎺掍负9锛屼簲涓厓绱犵殑閿欐帓涓44銆傞敊鎺掑叿鏈夌畝鍗曠殑璁＄畻鍏紡锛欴(n) = (n-1) [D(n-2) + D(n-1)]璁＄畻杩囩▼濡備笅锛欴锛1锛=0D锛2锛=1D锛3锛=2锛0+1锛=2D锛4锛=3锛2+1锛=9D锛5锛=4锛9+2锛=44 ...
