2003 AMC 8 第 16 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

16.

Ali、Bonnie、Carlo 和 Dianna 将一起开车去附近的主题公园。他们使用的车有四个座位:一个驾驶座、一个前排乘客座和两个后排座位。只有 Bonnie 和 Carlo 会开这辆车。有多少种可能的座位安排?

Ali, Bonnie, Carlo and Dianna are going to drive together to a nearby theme park. The car they are using has four seats: one driver’s seat, one front passenger seat and two back seats. Bonnie and Carlo are the only two who can drive the car. How many possible seating arrangements are there?

22

44

66

1212

2424

答案:D
知识点:有限制的排列乘法原理
难度评级:1230
解答:

驾驶座有 22 种选择。另一个前排座位有 33 种选择,第一个后排座位有 22 种选择。

最后一个人必须坐最后一个座位,所以共有 种座位安排。 232=12 2 \cdot 3 \cdot 2 = 12

所以正确答案是 D

There are 22 options for who sits in the driver's seat. There are 33 options for the other front seat, and 22 options for the first back seat.

The last person has to sit in the last seat, for a total of 232=12 2 \cdot 3 \cdot 2 = 12 possible seating arrangements.

Thus, D is the correct answer.

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