Question

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) 1/2

(b) 1/3

(c) 2/5

(d) 1/5

Answer 1

The correct option is (c) 2/5

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 ∩ E) = (4!) x (2!)⁵ 

Even when each American man is seated adjacent to his wife.

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