Question

泽塔先生和夫人想给孩子取名，使其姓名首字母组合（名、中间名、姓的首字母）按字母顺序排列且没有重复字母。这样的首字母组合有多少种？

Mr. and Mrs. Zeta want to name their baby Zeta so that its monogram (first, middle, and last initials) will be in alphabetical order with no letters repeated. How many such monograms are possible?

$276$

$300$

$552$

$600$

$15600$

答案：B

知识点：组合有限制的排列

难度评级：1470

小提示：

姓氏首字母已确定为 $Z$

The last initial is already fixed as $Z$

大提示：

选出另外两个不同字母后，其字母顺序就已确定

Choosing the other two distinct letters determines their alphabetical order

解答：

前两个首字母必须从 $A$ 到 $Y$ 中选取两个不同字母。一旦选定，顺序也随之确定。因此首字母组合数为 $\binom{25}{2}=300\text{。}$

所以正确答案是 B。

The first two initials must be two distinct letters chosen from $A$ through $Y.$ Once chosen, their order is forced. Therefore the number of monograms is $\binom{25}{2}=300.$

Thus the correct answer is B.

1989 AMC 12 第 9 题

答案：B

难度评级：1470

小提示：

大提示：

解答：

其他年份的第 9 题