AMC10 2003 B

AMC10 2003 B · Q10

AMC10 2003 B · Q10. It mainly tests Basic counting (rules of product/sum).

Nebraska, the home of the AMC, changed its license plate scheme. Each old license plate consisted of a letter followed by four digits. Each new license plate consists of three letters followed by three digits. By how many times is the number of possible license plates increased?

内布拉斯加州（AMC 的家乡）改变了其车牌方案。旧车牌由一个字母后跟四个数字组成。新车牌由三个字母后跟三个数字组成。新车牌可能数量是旧车牌的多少倍？

(A) 26^{10} 26^{10}

(B) 26^2 · 10^2 26^2 · 10^2

(D) 26^3 · 10^3 26^3 · 10^3

(E) 26^3 · 10^2 26^3 · 10^2

Answer

Correct choice: (C)

正确答案：（C）

Solution

(C) In the old scheme $26 \times 10^4$ different plates could be constructed. In the new scheme $26^3 \times 10^3$ different plates can be constructed. There are $\dfrac{26^3 \times 10^3}{26 \times 10^4}=\dfrac{26^2}{10}$ times as many possible plates with the new scheme.

（C）在旧方案中，可以构造 $26 \times 10^4$ 种不同的车牌。在新方案中，可以构造 $26^3 \times 10^3$ 种不同的车牌。因此，新方案下可用车牌数量是 $\dfrac{26^3 \times 10^3}{26 \times 10^4}=\dfrac{26^2}{10}$ 倍。

Topics

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