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MathematicsSingle correct+3 / -1Question 47 of 66

IIT-JEE 2007 · Paper 1, Mathematics question 47

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

Choose one option
Answer and worked solution

Official answer: C

Given event. Glue each American couple into a block (2 internal orders each). With the Indian man and his wife separate there are 6 units around the table: 5!⋅245!\cdot2^4 arrangements.

Both events. Gluing the Indian couple as well leaves 5 units: 4!⋅254!\cdot2^5 arrangements.

Conditional probability.
4!⋅255!⋅24=25.\frac{4!\cdot2^5}{5!\cdot2^4}=\frac25.

(C)

Topics:Conditional probabilityDistribution and arrangements
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