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? 

Answer 1

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) = \[\frac{^{2}{}{C}_2}{^{4}{}{C}_2} = \frac{1}{2 \times 3} = \frac{1}{6}\]