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      Question

      5 boys and 3 girls are to be seated on chairs arranged in a

      row. If the arrangement is made at random, find the probability that no two girls will be seated next to one another.
      A 5/14 Correct Answer Incorrect Answer
      B 1/3 Correct Answer Incorrect Answer
      C 5/16 Correct Answer Incorrect Answer
      D 5/12 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      8 people can be seated on 8 chairs in 8! ways.

      No two girls will be seated next to one another, so the arrangement would be like:

      __ B __ B __ B __ B __ B __

      5 boys can be seated at 5 places in 5! Ways. After this, 3 girls can be seated in the remaining 6 places in  6 P 3  ways.

      Favorable outcomes= 5! X  6 P 3 .

      Probability = (5! x 6!)/(3! x 8!) = 5/14

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