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