[問題] 離散考古2005M2
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
→
10/28 21:32, , 1F
10/28 21:32, 1F
→
10/28 21:33, , 2F
10/28 21:33, 2F
推
10/28 21:39, , 3F
10/28 21:39, 3F
推
10/28 22:18, , 4F
10/28 22:18, 4F
推
10/28 22:47, , 5F
10/28 22:47, 5F
推
10/28 23:19, , 6F
10/28 23:19, 6F
→
10/28 23:46, , 7F
10/28 23:46, 7F