Six mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie’s requirement is satisfied? A.6 B.24 C.120 D.360 E.720 解释：Ignoring Frankie's requirement for a moment, observe that the six mobsters can be arranged 6! or 6 x 5 x 4 x 3 x 2 x 1 = 720 different ways in the concession stand line. In each of those 720 arrangements, Frankie must be either ahead of or behind Joey. Logically, since the combinations favor neither Frankie nor Joey, each would be behind the other in precisely half of the arrangements. Therefore, in order to satisfy Frankie's requirement, the six mobsters could be arranged in 720/2 = 360 different ways. The correct answer is D. 划线部分没有明白 我当时的思路是 1. Joey站在第一个或最后一个 2x4! 2. Joey不在第一个也不在最后一个 4x2x4! 加起来答案是240 orz。。 -- by 会员 alexayin (2011/6/28 8:11:20)
划线的意思是说F和J 互相在对方后面的组合是一样的，
题目的意思是6个位置组成一条竖线，其中J必须在F的前面（可以不挨着）。这样J在F前面的所有组合正好等于J在F后面的所有组合
你的思路第一条就违反了要求，如果J在最后一排的话就无法使得J在F前面。
也有个笨办法，
1. J在第一位，则其余5人随便坐都可以保证J在F前，A（5,5）
2. J在第二位，则F必须在其后面的4位选一个，其余4人随便坐，C(1,4)*A(4,4)
3. J在第三位，则F必须在其后面的3位选一个，其余4人随便坐，C(1,3)*A（4,4）
4 。。。。。。。。。。。。。。。。。。。。。。。。。。。 C（1,2）*A（4,4)
5............................................................................................... A(4 ,4)
再相加，这个思路能否理解 | 
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发表于 2011-6-28 08:11:20
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