10 persons are seated at a round table. What is the probability that two particular persons sit together ?

Options

A. 2/7
B. 3/7
C. 4/9
D. 2/9

Explanation

n (S) = no. of ways of sitting 10 persons at round table = (10 – 1) ! = 9 since 2 particular persons will be always together. Then the no. of persons = 8 + 1 = 9.
`therefore` 9 persons will be seated in `(9 – 1) ! = 8 !` ways at round table and 2 particular persons will be seated themselves in` 2 !` ways
therefore The number of ways in which two persons always sit together at round table `= 8! 2! = n (E)`
P(E)= `(n(E))/(n(S))=(8!xx2!)/(9!)`
`=(8!xx2)/(9xx8!)=2/9`