InterviewSolution
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InterviewSolution
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Six boys and six girls sit in a row randomly. Find the probability that (i) The six girls sit together (ii) The boys and girls sit alternately. |
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Answer» (i) 6 boys and 6 girls sit in a row randomly. Total ways of their seating = 12! No. of ways in which all the 6 girls sit together = 6! x 7! (Considering all 6 girls as one person) ∴ Probability of all girls sitting together = 6! x 7!/12! = 720/12 x 11 x 10 x 9 x 8 = 1/132 (ii) Staring with boy, boys can sit in 6! Ways leaving one place between every two boys and two one a last. B _ B _ B _ B _ B _ B _ These left over places can be occupied by girls in 6! ways. ∴ If we start, with boys. No. of ways of seating boys and girls alternately = 6! x 6! In the similar manner, if we start with girl, no. of ways of seating boys and girls alternately = 6! x 6! G _ G _ G _ G _ G _ G _ Thus total ways of alternate seating arrangements = 6! x 6! + 6! x 6! = 2 x 6! x 6! ∴ Probability of making alternate seating arrangement for 6 boys and 6 girls = 2 x 6! x 6!/12! = 2 x 720/12 x 11 x 10 x 9 x 8 x 7 = 1/462 |
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