WAEC Further Mathematics 2022 Paper

Concept:Pairing six persons means dividing all six into three unordered pairs of two.Explanation:Select the first pair from 6 persons: $\binom{6}{2}=15$ ways.Select the second pair from the remaining 4 persons: $\binom{4}{2}=6$ ways.The last 2 persons automatically form the third pair: $\binom{2}{2}=1$ way.Since the order of the three pairs does not matter, divide by $3!$.Therefore, the number of ways is:$$\frac{6!}{(2!)^3 3!} = \frac{720}{8 \times 6} = 15.$$This matches the process $\frac{\binom{6}{2}\binom{4}{2}\binom{2}{2}}{3!}=15$.Answer:C. 15