# One Indian and four American men and their wives are to be seated randomly around a circular table.

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One 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 his wife given that each American man is seated adjacent to his wife is

(a) $\frac{1}{2}$

(b) $\frac{1}{3}$

(c) $\frac{2}{5}$

(d) $\frac{1}{5}$

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Answer: (C) =$\frac{2}{5}$

Let A: Event that Indian man is seated adjacent to his wife.

Let B: Event that each American is seated adjacent to his wife.

Consider each couple as one entity. Thus, there are 5 entities to be arranged and husbands and wife can interchange their seats in 2! ways.

∴ $P(A\,\cap\,B)$ = $\frac{4!(2!)^5}{9!}$

Next, consider each American couple as an entity. Thus, there are 6 entities to be arranged including the Indian and his wife.

∴ P(B) = $\frac{5!(2!)^4}{9!}$