2. 外语
  3. 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

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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：A55=120种不同的排列方式；小明和小刚相邻：A44×A33=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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