Bunuel wrote:

A committee of three must be formed from 5 women and 5 men. What is the probability that the committee will be exclusive to one gender?

(A) 1/60

(B) 1/120

(C) 1/8

(D) 1/6

(E) 1/3

Kudos for correct solution.

Here total number of members (men and women) = 10

NOw we need to choose 3 out of these. Again favourable events to one gender will be 5C3 (since both men and women are 5 in numbers)

Since

probability = \frac{No. of favourable events}{Total possible outcomes}i.e

probability = \frac{5C3}{10C3} + \frac{5C3}{10C3} (we have taken two times 5C3 because we need to have exclusive to one gender i.e either men or women, so combining them will give us total number of favorable events)

= \frac{1}{12} +\frac{1}{12} =\frac{1}{6}
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