Question

$2020$ 到 $2400$ 之间有多少个整数的四个数字互不相同且按递增顺序排列？（例如 $2357$ 是一个这样的整数。）

How many integers between $2020$ and $2400$ have four distinct digits arranged in increasing order? (For example, $2357$ is one integer.)

$9$

$10$

$15$

$21$

$28$

知识点：数字组合

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千位必须是 $2$ 。因为数字互不相同且递增，百位必须是 $3$ 。

最后两位必须从 $4,5,6,7,8,9$ 中选择；选定两个数字后，它们的顺序也就确定了。

共有 $\binom{6}{2}=15$ 个这样的整数。

正确答案是 C。

The thousands digit must be $2.$ Since the digits are distinct and increasing, the hundreds digit must be $3.$

The last two digits must be chosen from $4,5,6,7,8,9.$ Once the two digits are chosen, their order is forced.

There are $\binom{6}{2}=15$ such integers.

Thus, the correct answer is C.