2. 外语
  3. In how many ways can Ann, Bob, Chunk, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?

In how many ways can Ann, Bob, Chunk, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?

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问题 In how many ways can Ann, Bob, Chunk, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?
选项 A、24
B、48
C、56
D、72
E、96
答案D
解析 5个人所有排列的情况减去Ann和Bob相邻的情况，就是不相邻的情况。5个人的全排列是A55。若A和B相邻：
(1)把AB视为1个整体，则AB、C、D、E做排列，即有A44种情况；
(2)A和B内部又有AB和BA两种排列方式，即有A22种情况。因此，AB相邻的情况，用乘法原理可得共有A44A22种。则AB不相邻的情况共有A55-A44A22=72种。所以答案为D选项。
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