AMC 8 2003 Problem 16

AMC8 2003 年第 16 题

排列与组合★★★☆☆

Ali, Bonnie, Carlo, and Dianna are going to drive together to a nearby theme park. The car they are using has 4 seats: 1 Driver seat, 1 front passenger seat, and 2 back passenger seats. Bonnie and Carlo are the only ones who know how to drive the car. How many possible seating arrangements are there?

Ali，Bonnic，Carlo 和 Dianna 将一起开车去附近的一个主题公园。他们使用的汽车有 4 个座椅：1 个驾驶员座椅、1 个前排乘客座椅和 2 个后排乘客座椅。车上只有 Bonnie 和 Carlo 会开车。则有多少种可能的安排座位的方法？

A.2
B.4
C.6
D.12
E.24

正确答案 · Correct Answer

解析 · Solution

Solution 1

There are only 2 people who can go in the driver's seat--Bonnie and Carlo. Any of the 3 remaining people can go in the front passenger seat. There are 2 people who can go in the first back passenger seat, and the remaining person must go in the last seat. Thus, there are

2\cdot3\cdot2

or 12 ways. The answer is then 12. If there weren't any extra requirements, there would be 24 combinations. However, there are only 2, which is half of 4, ways to put the people for the first seat by restriction. Therefore, half of 24 is 12. Solution by ILoveMath31415926535

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