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      Question

      6 Boys and 5 Girls sat in a row randomly. What is the

      probability that no 2 Girls are together?
      A 1/22 Correct Answer Incorrect Answer
      B 1/11 Correct Answer Incorrect Answer
      C 2/11 Correct Answer Incorrect Answer
      D 2/21 Correct Answer Incorrect Answer
      E 1/21 Correct Answer Incorrect Answer

      Solution

      6 Boys and 5 Girls, i.e., a total of 11 people can be arranged in 11!/6!5! ways or, 462 ways.

      For no 2 Girls to sit together, arrangement can be done in the following way: [B are Boys]

      _ B _ B _ B _ B _ B _B_

      There are 7 spaces that can be taken up by 5 Girls so that no 2 of them sit together.

      Number of ways =  7 C 5  = 21.

      Required probability = 21/462 = 1/22

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