2003 AMC 8 第 16 题

先试着解答 2003 AMC 8 第 16 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2003 AMC 8 解答,或核对答案。

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
小提示:
先选择驾驶员
Choose the driver first.
大提示:
选定驾驶员后,将另外三个人安排到剩余座位
After the driver is chosen, arrange the other three people in the remaining seats.
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 2⋅3⋅2=12 2 \cdot 3 \cdot 2 = 12 种座位安排。
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 2⋅3⋅2=12 2 \cdot 3 \cdot 2 = 12 possible seating arrangements.
Thus, D is the correct answer.
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