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 E= event when each American man is seated adjacent to his wife
and A=event when Indian man is seated adjacent to his wife
Now , `n(A cap E ) =(4!) xx (2!)^(5)`
Even when each American man is seated adjacent to his wife.
Again , ` n(E)=(5!)xx(2!)^(4)`
`:. P""((A)/(E)) =(n(A cap E ))/(n(E)) =((4!)xx(2!)^(5))/((5!)xx(2!)^(4))=(2)/(5)`
Alternate solution
Fixing four American couples and one Indian man in between any two couples , we have 5 different ways in which his wife can be seated , of which 2 cases are favourable.
`:.` Required probability `=(2)/(5)`