AMC8 2015

AMC8 2015 · Q4

AMC8 2015 · Q4. It mainly tests Basic counting (rules of product/sum), Permutations.

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?

Centerville中学的象棋队由两名男孩和三名女孩组成。摄影师想为当地报纸拍摄团队照片。她决定让他们坐成一排，两端各坐一名男孩，中间坐三名女孩。有多少种这样的排列方式？

(A) 2 2

(B) 4 4

(D) 6 6

(E) 12 12

Answer

Correct choice: (E)

正确答案：（E）

Solution

Answer (E): There are 2 ways to seat the boys, one on each end, and $(3\cdot2\cdot1=6)$ ways to seat the three girls in the middle. So there are $(2\cdot6=12)$ possible arrangements.

答案（E）：男孩坐在两端（每端一个）有 2 种坐法；三个女孩坐在中间有 $(3\cdot2\cdot1=6)$ 种排列方式。因此一共有 $(2\cdot6=12)$ 种可能的安排。

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