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我是这样推的!!!!

Posted by crackerwang at 2007-10-26 15:51:25 on Problem 1354
In Reply To:这题。。公式怎么得出来的? Posted by:Roba at 2006-11-06 16:16:03
我推的是打不开的情况..
打不开的情况其实就是k个盒子里面放的 是这K个盒子上对应的锁..所以就算把这k个盒子全打开了也拿不到剩下盒子的钥匙
一共是k!种方法..
所以不能打开所有的情况其实就是n-1个盒子里放的钥匙刚好对应的是这n-1个盒子上的锁
从n-2个里面选出n-3个和1,2够成了了n-1个盒子.
总数=c(n-2,n-3)*(n-1)!;
答案=n!-总数=2*(n-1)!;

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