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Ming and Gang are both so talkative such that they will affect other classmates if they seat together. Now there are 5 people in
Ming and Gang are both so talkative such that they will affect other classmates if they seat together. Now there are 5 people in
admin
2020-05-11
24
问题
Ming and Gang are both so talkative such that they will affect other classmates if they seat together. Now there are 5 people in this class including Ming and Gang seating in a row. How many ways are there for the seat arrangement if Ming and Gang do not seat together?
选项
A、24
B、48
C、56
D、72
E、96
答案
D
解析
5个人排座位,没有其他限制条件,则只包括小明(Ming)和小刚(Gang)“相邻”和“不相邻”这两种情况。这道题目要求小明和小刚“不相邻”,可以先计算小明和小刚相邻的情况数量,再用5个人的全排列数减去相邻的情况数量,得到他们不相邻的情况数量。5个人全排列:A
5
5
=120种不同的排列方式;小明和小刚相邻:A
4
4
×A
3
3
=48种不同的排列方式;故小明和小刚不相邻的情况有120-48=72种,选D。
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