AMC12 2006 B

AMC12 2006 B · Q7

AMC12 2006 B · Q7. It mainly tests Basic counting (rules of product/sum).

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?

Lopez 先生和 Lopez 太太有两个孩子。当他们坐进家庭用车时，两人坐在前排，另外两人坐在后排。Lopez 先生或 Lopez 太太必须坐在驾驶座。有多少种可能的座位安排？

(A) 4 4

(B) 12 12

(D) 24 24

(E) 48 48

Answer

Correct choice: (B)

正确答案：（B）

Solution

First, we seat the children. The first child can be seated in $3$ spaces. The second child can be seated in $2$ spaces. Now there are $2 \times 1$ ways to seat the adults. $3 \times 2 \times 2 = 12 \Rightarrow \text{(B)}$

先安排孩子就座。第一个孩子可以坐在 $3$ 个位置中的任意一个。第二个孩子可以坐在剩下的 $2$ 个位置中的任意一个。此时成人就座有 $2 \times 1$ 种方式。 $3 \times 2 \times 2 = 12 \Rightarrow \text{(B)}$

Topics

CP.001 Basic counting (rules of product/sum)