Question

兔子 Peter 和 Pauline 有三个孩子 Flopsie、Mopsie 和 Cottontail。现在要把这五只兔子分配给四家不同的宠物店，使得没有一家店同时得到一只父母兔和一只孩子兔。不要求每家店都得到兔子。有多少种不同的分配方法？

Rabbits Peter and Pauline have three offspring—Flopsie, Mopsie, and Cottontail. These five rabbits are to be distributed to four different pet stores so that no store gets both a parent and a child. It is not required that every store gets a rabbit. In how many different ways can this be done?

$96$

$108$

$156$

$204$

$372$

答案：D

知识点：分类讨论乘法原理

难度评级：1880

解答：

如果两只父母兔在同一家店，有 $4$ 种选择，而每只孩子兔必须去另外三家店之一：共有 $4\cdot 3^3 = 108$ 种。

如果父母兔去不同的店，有 $4\cdot 3 = 12$ 种选择，而每只孩子兔必须去剩下两家店之一：共有 $12\cdot 2^3 = 96$ 种。

总数为 $108 + 96 = 204$ 。

因此，正确答案是 D。

If the two parents share a store, there are $4$ choices for it, and each child must go to one of the other three stores: $4\cdot 3^3 = 108$ ways.

If the parents go to different stores, there are $4\cdot 3 = 12$ choices, and each child must go to one of the two remaining stores: $12\cdot 2^3 = 96$ ways.

The total is $108 + 96 = 204.$

Thus, the correct answer is D.

2013 AMC 12A 第 15 题

答案：D

难度评级：1880

解答：

其他年份的第 15 题