Question

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

A) 3/91 B) 2/73 C) 1/91 D) 3/73

Answer 1

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