作者zenixls2 (zenix)
看板b98902HW
標題[問題] 離散考古2005M2
時間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
以上這兩題
高中排容忘的差不多了，第七題希望可以給詳細的式子
第11題只要給(b)的做法
(我發現我只要題目稍有變化就做不太出來了QQ)
解A(x)解不太出來...
感激不盡
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.241.21
1F：→ davll:這篇文應該放在b97HW板上會比較快回文 10/28 21:32
2F：→ zenixls2:其實也可以放math版啦... 10/28 21:33
3F：推 chengweiwei:原來是這兩題..我好像會 但是考完試了..你還想知道嗎? 10/28 21:39
4F：推 lmr3796:這題用rook其實不錯好做 10/28 22:18
5F：推 bombom:rook是什麼??? 10/28 22:47
6F：推 clywin123:第七題考慮 不取p 取一個p 取兩個p來做 10/28 23:19
7F：→ zenixls2:第十一題哩??用老師講的方法好像甚麼都做不出來 10/28 23:46