Question

有多少个三位正整数的数位和等于 $25$ ？

For how many three-digit whole numbers does the sum of the digits equal $25?$

$2$

$4$

$6$

$8$

$10$

数位和为 $25$ ，而最大可能和是 $27$ ，所以至少有一个数字是 $9$ 。可能的数字组是 $\{9, 9, 7\}$ 和 $\{9, 8, 8\}$ 。

每组都有 $3$ 种不同排列： $997, 979, 799$ 以及 $988, 898, 889$ ，共 $6$ 个数。

所以正确答案是 C。

Since the digits sum to $25$ and the maximum is $27$ , at least one digit is $9$ . The possible digit sets are $\{9, 9, 7\}$ and $\{9, 8, 8\}.$

Each set has $3$ distinct arrangements ( $997, 979, 799$ and $988, 898, 889$ ), giving $6$ numbers in all.

Thus, the correct answer is C .