2015 AMC 8 第 15 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。
15.
在欧拉中学， 名学生对学校公投中的两个议题进行了投票，结果如下： 人支持第一个议题， 人支持第二个议题。如果正好有 名学生两个议题都反对，那么有多少名学生两个议题都支持？
At Euler Middle School, students voted on two issues in a school referendum with the following results. voted in favor of the first issue and voted in favor of the second issue. If there were exactly students who voted against both issues, how many students voted in favor of both issues?
答案：D
小提示：
先求有多少学生至少支持一个议题
First find how many students voted for at least one issue.
大提示：
对两个支持人数使用容斥原理
Use inclusion-exclusion on the two yes-vote counts.
视频讲解：
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文字解答：
因为 名学生两个议题都反对，所以 名学生至少支持一个议题。
已知 人支持第一个议题， 人支持第二个议题，且 人至少支持一个议题。由容斥原理，两个都支持的人数为
所以正确答案是 D。
Since students voted against both, we know that people voted for at least one.
As we know that students voted for the first issue, and students voted for the second issue, and students that voted for at least one issue, we conclude that the number of students that voted for both is
Thus, the correct answer is D .
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