2015 AMC 8 第 4 题

先试着解答 2015 AMC 8 第 4 题,然后核对你的答案与视频与精心整理的解答,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 2015 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。

4.

森特维尔中学国际象棋队由两名男生和三名女生组成。一位摄影师想为当地报纸拍一张队伍照片。她决定让他们坐成一排,两端各坐一名男生,中间坐三名女生。这样的排列有多少种?
The Centerville Middle School chess team consists of two boys and three girls. A photographer wants to take a picture of the team to appear in the local newspaper. She decides to have them sit in a row with a boy at each end and the three girls in the middle. How many such arrangements are possible?
22
44
55
66
1212
答案:E
知识点:排列乘法原理
小提示:
先把两名男生放在两端
Place the two boys at the two ends first.
大提示:
再排列中间三个座位上的女生
Then arrange the three girls in the middle seats.
视频讲解:
解答视频缩略图
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文字解答:
两名男生坐在两端有 2!=22! = 2 种方式。三名女生坐在中间三个座位有 3!=63! = 6 种方式。
因此总排列数为 2⋅6=122\cdot6=12。
所以正确答案是 E。
There are 2!=22! = 2 ways to place the two boys at the two ends. There are 3!=63! = 6 ways to arrange the three girls in the middle seats.
Thus the total number of arrangements is 2⋅6=12.2\cdot6=12.
Thus, E is the correct answer.
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