AMC8 2003

AMC8 2003 · Q16

AMC8 2003 · Q16. It mainly tests Basic counting (rules of product/sum), Permutations.

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?

Ali、Bonnie、Carlo 和 Dianna 要一起开车去附近的游乐园。他们使用的汽车有四个座位：一个驾驶座、一个前排乘客座和两个后排座位。只有 Bonnie 和 Carlo 会开车。有多少种可能的座位安排？

(A) 2 2

(B) 4 4

(D) 12 12

(E) 24 24

Answer

Correct choice: (D)

正确答案：（D）

Solution

There are 2 choices for the driver. The other three can seat themselves in $3 \times 2 \times 1 = 6$ different ways. So the number of seating arrangements is $2 \times 6 = 12$.

驾驶员有 2 个选择。其余三人可以以 $3 \times 2 \times 1 = 6$ 种不同的方式就座。因此，座位安排的数量是 $2 \times 6 = 12$。

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