SOA 的 Exam P Sample 第247题。

SOA P Sample Q247 : Each week, a subcommittee of four individuals is formed from among the members of a committee comprising seven individuals. Two subcommittee members are then assigned to lead the subcommittee, one as chair and the other as secretary.

Calculate the maximum number of consecutive weeks that can elapse without having the subcommittee contain four individuals who have previously served together with the same subcommittee chair.

    1. 70
    1. 140
    1. 210
    1. 420
    1. 840

思路

题目的意思是,7个人里选4个人出来组成一组。对选出的四个人的其中两个给以特定的身份:chair 和 secretary. 求出不同的组合方法有几种。

刚开始看题的时候我也想当然地列了这个式子: \[ A_7^2\times C_5^2=420 \] 刚好掉进了题目给挖的坑里。

实际上,题目的最后说了,只要没有“served together with the same subcommittee chair”,就可以算是不同的组合方法。所以跟秘书(secretary)是谁没有关系。因此我们可以直接把题目理解为:7选4,指定其中一人为 chair,求出不同的组合方法共几种。所以先在7个人中选出1个人担任 chair,然后在其余6人中选出3人即可: \[ A_7^1\times C_6^3=140 \]

答案

所以选 (B) 140

精算每日一题专栏

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