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?

Answer 1

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) =\[\frac{^{2}{}{C}_1 \times ^{2}{}{C}_1}{^{4}{}{C}_2} = \frac{2 \times 2}{2 \times 3} = \frac{2}{3}\]