Indian and four American men and their wives are to be seated randomly around a circular table. Then, the conditional probability that the Indian man is seated adjacent to this wife given that each American man is seated adjacent to his wife is `1//2` b. `1//3` c. `2//5` d. `1//5`

Options

A. `(1)/(2)`
B. `(1)/(3)`
C. `(2)/(5)`
D. `(1)/(5)`

Answer

C

Explanation

Let A denote the event that each American man is seated adjacent to his wife and B denote the event that Indian man is seated adjacent to his wife. Then,
Required probability `=P(B//A)`
Number of ways in which Indian man sits
adjacent to his wife when each man is seated adjacents
`=("to his wife")/("Number of ways in which each American man is seated adjacent to his wife")`
`=((2!)^(5)xx(5-1)!)/((2!)^(4)(6-1)!)=(2)/(5)`