2006 AMC 12B 第 7 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。

7.

Lopez 先生和 Lopez 太太有两个孩子。他们上家庭汽车时,两个人坐在前排,另外两个人坐在后排。 Lopez 先生或 Lopez 太太必须坐在驾驶座。共有多少种座位安排?

Mr. and Mrs. Lopez have two children. When they get into their family car, two people sit in the front, and the other two sit in the back. Either Mr. Lopez or Mrs. Lopez must sit in the driver's seat. How many seating arrangements are possible?

44

1212

1616

2424

4848

答案:B
知识点:乘法原理有限制的排列
难度评级:1180
解答:

驾驶员是两位父母之一:有 22 种选择。

剩下的 33 人中任意一人可以坐副驾驶座,最后 22 人坐后排,有 22 种顺序。

总数为 232=122 \cdot 3 \cdot 2 = 12

因此,正确答案是 B

The driver is one of the two parents: 22 choices.

Any of the remaining 33 people can sit in the front passenger seat, and the last 22 people fill the back in 22 orders.

The total is 232=12.2 \cdot 3 \cdot 2 = 12.

Thus, the correct answer is B.

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