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

a) 2/9 b)1/13 c)2/13 d)1/26

• Answer : d) 1/26
  
  Solution :
  
  In a circle of n different persons, the total number of arrangements possible = (n - 1)!
  Total number of arrangements = n(S) = (14 – 1)! = 13 !
  Taking three persons as a unit, total persons = 12 (in 4 units)
  Therefore no. of ways for these 12 persons to around the circular table = (12 - 1)! = 11!
  In any given unit, 3 particular person can sit in 3!. Hence total number of ways that any three person can sit =
  n(E) = 11! X 3!
  Therefore P (E) = probability of three persons sitting together = n(E) / n(S) = 11! X 3 ! divided by 13!
  3 x 2 divided by 13 x 12 = 1/26
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