Question

大卫的所有电话号码形如 $555\text{–}abc\text{–}defg$ ，其中 $a, b, c, d, e, f$ 和 $g$ 是互不相同且按递增顺序排列的数字，并且都不是 $0$ 或 $1$ 。大卫可能有多少个不同的电话号码？

All of David's telephone numbers have the form $555\text{–}abc\text{–}defg,$ where $a, b, c, d, e, f,$ and $g$ are distinct digits and in increasing order, and none is either $0$ or $1.$ How many different telephone numbers can David have?

$1$

$2$

$7$

$8$

$9$

答案：D

知识点：组合双射

难度评级：1510

解答：

这七个数字从集合 $\{2, 3, 4, 5, 6, 7, 8, 9\}$ 中选择，且一旦选定就必须按递增顺序写出，所以只需要考虑选哪些数字。

从这八个数字中选择七个，等价于选择留下不用的那一个数字，共有 $8$ 种。

所以正确答案是 D。

The seven digits are chosen from $\{2, 3, 4, 5, 6, 7, 8, 9\},$ and once chosen they must be written in increasing order, so only the choice of digits matters.

Choosing seven of these eight digits is the same as choosing the one digit to leave out, which can be done in $8$ ways.

Thus, D is the correct answer.

2005 AMC 10B 第 18 题

答案：D

难度评级：1510

解答：

其他年份的第 18 题