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Question
A committee of two persons is selected from two men and two women. What is the probability that the committee will have no man?
Solution
Total number of people = 2 + 2 = 4
Out of these four people, two can be selected in 4C2 = 6 ways.
No man in the committee of two means that there will be two women in the committee.
Out of two women, two can be selected in 2C2 = 1 way.
∴ P(no man) = \[\frac{^{2}{}{C}_2}{^{4}{}{C}_2} = \frac{1}{2 \times 3} = \frac{1}{6}\]
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