2021 AMC 12B Spring 第 2 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
2.
在一次数学竞赛中， 名学生穿蓝衬衫，另外 名学生穿黄衬衫。这 名学生被分成 对。恰好有 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, students are wearing blue shirts, and another students are wearing yellow shirts. The students are assigned into pairs. In exactly of these pairs, both students are wearing blue shirts. In how many pairs are both students wearing yellow shirts?
小提示：
对全蓝组合用掉 名蓝衬衫学生
The all-blue pairs use blue students
大提示：
先数混合配对中剩下的蓝衬衫学生，再从黄衬衫学生中去掉同样的人数
Count the blue students left in mixed pairs, then remove that many yellow students
解答：
对全蓝组合用了 名蓝衬衫学生，还剩 名蓝衬衫学生。
这 名蓝衬衫学生每人都必须和一名黄衬衫学生配对，所以有 对混合组合，用掉 名黄衬衫学生。
剩下的 名黄衬衫学生组成 对全黄组合。
所以正确答案是 B。
The all-blue pairs account for blue students, leaving blue students.
Each of those blue students must be paired with a yellow student, so there are mixed pairs, using yellow students.
The remaining yellow students form all-yellow pairs.
Thus, the correct answer is B.
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