2. 外语
  3. In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated and the b

In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated and the b

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问题 In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated and the boys are not separated?
选项 A、24
B、36
C、72
D、144
E、288
答案C
解析 此题要求女生不分开，男生也不分开。即坐在一起，因此采用“捆绑法”，即把需要相邻的人看成一个整理。此题有两个整体：男生、女生。首先，由于是排座位，顺序重要，所以是排列问题。之后分成三个步骤。第一步将男生、女生两个整体进行排列，方案数为A22。第二步将3个男生在男生整体内部进行排列，方案数为A33。第三步将3个女生在女生整体内部进行排列，方案数也为A33。
所以总方案数是A22×A33×A33=72。故答案为C。
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