Question

在一次数学竞赛中， $57$ 名学生穿蓝衬衫，另外 $75$ 名学生穿黄衬衫。这 $132$ 名学生被分成 $66$ 对。恰好有 $23$ 对中的两名学生都穿蓝衬衫。有多少对中的两名学生都穿黄衬衫？

At a math contest, $57$ students are wearing blue shirts, and another $75$ students are wearing yellow shirts. The $132$ students are assigned into $66$ pairs. In exactly $23$ of these pairs, both students are wearing blue shirts. In how many pairs are both students wearing yellow shirts?

$23$

$32$

$37$

$41$

$64$

答案：B

知识点：基本计数奇偶性

难度评级：1040

解答：

$23$ 对全蓝组合用了 $46$ 名蓝衬衫学生，还剩 $57 - 46 = 11$ 名蓝衬衫学生。

这 $11$ 名蓝衬衫学生每人都必须和一名黄衬衫学生配对，所以有 $11$ 对混合组合，用掉 $11$ 名黄衬衫学生。

剩下的 $75 - 11 = 64$ 名黄衬衫学生组成 $64 \div 2 = 32$ 对全黄组合。

所以正确答案是 B。

The $23$ all-blue pairs account for $46$ blue students, leaving $57 - 46 = 11$ blue students.

Each of those $11$ blue students must be paired with a yellow student, so there are $11$ mixed pairs, using $11$ yellow students.

The remaining $75 - 11 = 64$ yellow students form $64 \div 2 = 32$ all-yellow pairs.

Thus, the correct answer is B.

2021 AMC 12B Spring 第 2 题

答案：B

难度评级：1040

解答：

其他年份的第 2 题