作者zenixls2 (zenix)
看板b98902HW
标题[问题] 离散考古2005M2
时间Wed Oct 28 17:34:15 2009
7. Find the number of way to arrange the letters in LAPTOP so that none of the
letters L, A, T, O is in its original position and the letter P is not in the
third or sixth position.
ANS:84
11. Find recurrence relations for the following.
(a) The number of ways to fully parenthesize w1+w2+ … +wn.
(For example, there are two ways, ((w1＋w2)＋w3) and (w1＋(w2＋w3)), to
parenthesize w1＋w2＋w3.)
(b) The number of derangements of 1, 2, …, n.
ANS:(a) a = a * a + a * a + .... a * a ,a =1,a =1,a =2
n 1 n-1 2 n-2 n-1 1 1 2 3
(b) a = n! - nC1 * (n-1)! + nC2 * (n-2)! + ... nCn * 0!
n
以上这两题
高中排容忘的差不多了，第七题希望可以给详细的式子
第11题只要给(b)的做法
(我发现我只要题目稍有变化就做不太出来了QQ)
解A(x)解不太出来...
感激不尽
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1F：→ davll:这篇文应该放在b97HW板上会比较快回文 10/28 21:32
2F：→ zenixls2:其实也可以放math版啦... 10/28 21:33
3F：推 chengweiwei:原来是这两题..我好像会 但是考完试了..你还想知道吗? 10/28 21:39
4F：推 lmr3796:这题用rook其实不错好做 10/28 22:18
5F：推 bombom:rook是什麽??? 10/28 22:47
6F：推 clywin123:第七题考虑 不取p 取一个p 取两个p来做 10/28 23:19
7F：→ zenixls2:第十一题哩??用老师讲的方法好像甚麽都做不出来 10/28 23:46