1991 AMC 8 第 23 题
先试着解答 1991 AMC 8 第 23 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1991 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
23.
毕达哥拉斯高中的乐队有 名女生和 名男生。毕达哥拉斯高中的管弦乐队有 名女生和 名男生。有 名女生同时属于乐队和管弦乐队。总共有 名学生属于乐队或管弦乐队或两者都属于。属于乐队但不属于管弦乐队的男生人数是
The Pythagoras High School band has female and male members. The Pythagoras High School orchestra has female and male members. There are females who are members in both band and orchestra. Altogether, there are students who are in either band or orchestra or both. The number of males in the band who are NOT in the orchestra is
小提示：
先用 求属于至少一个团体的女生人数
First find how many females are in at least one group, using
大提示：
用总人数 减去女生人数，得到属于至少一个团体的男生人数；再用容斥原理求同时属于两个团体的男生人数
Subtract the females from the total to get the males in at least one group, then use inclusion–exclusion to find how many males are in both groups
解答：
属于乐队或管弦乐队的女生人数为 。所以属于至少一个团体的男生人数为 。
乐队有 名男生，管弦乐队有 名男生，因此两个团体都有的男生人数是 。属于乐队但不属于管弦乐队的男生有 人。
所以正确答案是 A。
Females in band or orchestra: So males in at least one group:
With males in band and in orchestra, the males in both are Hence males in band but not orchestra:
Thus, the correct answer is A .
其他年份的第 23 题
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