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  • Question
  • fifteen persons are sitting around a circular table facing the centre. What is the probability that three particular persons sit together ?


  • Options
  • A. 3/91
  • B. 2/73
  • C. 1/91
  • D. 3/73

  • Correct Answer
  • 3/91 

    Explanation

    In a circle of n different persons, the total number of arrangements possible = (n - 1)!
    Total number of arrangements = n(S) = (15 ? 1)! = 14 !
    Taking three persons as a unit, total persons = 13 (in 4 units)
    Therefore no. of ways for these 13 persons to around the circular table = (13 - 1)! = 12!
    In any given unit, 3 particular person can sit in 3!. Hence total number of ways that any three person can sit =
    n(E) = 12! X 3!
    Therefore P (E) = probability of three persons sitting together = n(E) / n(S) = 12! X 3 ! / 14!
    = 12!x3x2 / 14x13x12! = 6/14x13 = 3/91

  • Tags: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO

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