[問題] 離散考古2005M2

[zenixls2 (zenix)]

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

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→ davll:這篇文應該放在b97HW板上會比較快回文
→ zenixls2:其實也可以放math版啦...
推 chengweiwei:原來是這兩題..我好像會 但是考完試了..你還想知道嗎?
推 lmr3796:這題用rook其實不錯好做
推 bombom:rook是什麼???
推 clywin123:第七題考慮 不取p 取一個p 取兩個p來做
→ zenixls2:第十一題哩??用老師講的方法好像甚麼都做不出來