63. A,O,L,L,P排列五字母组合,问两个L至少隔开一个位置有多少种可能? 我的答案: 72 P(5,5)-C(2,1)P(4,4), C(2,1)P(4,4)是两个L连在一个位置的可能
I think the right answer is 36. The two Ls are indistinguishable. The total number of 五字母组合 is not P(5, 5), instead, it is P(5,5)/2. P(4,4)是两个L连在一个位置的可能. P(5,5)/2 - P(4,4) = 36 There is another way to get the right answer. Treat this problem in this way. X A X O X P X Select 2 X from the 4 Xs for the two Ls, so the Ls will be separated at least by one letter. The total number to select Xs is C(4, 2), while A, O, P can be arranged in P(3, 3) ways. So the final answer is C(4, 2) * P(3, 3) = 36.
[此贴子已经被作者于2006-9-13 7:59:31编辑过] |