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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 one man?
Solution
Total number of people = 2 + 2 = 4
Out of these four people, two can be selected in 4C2 = 6 ways.
One man in the committee of two means that there is one woman in the committee.
One man out of 2 can be selected in 2C1 = 2 ways.
One woman out of 2 can be selected in 2C1 = 2 ways.
Together, they can be selected in 2C1 × 2C1 ways.
∴ P (one man) =\[\frac{^{2}{}{C}_1 \times ^{2}{}{C}_1}{^{4}{}{C}_2} = \frac{2 \times 2}{2 \times 3} = \frac{2}{3}\]
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