NECO 2023 · Paper 1 · Q43

In how many ways can a committee of eight councillors be selected from ten councillors in a Local Government?

Worked solution (try it first)

A committee is a selection, so order doesn't matter: the count is $\binom{10}{8}$ .
Choosing 8 to serve is the same as choosing 2 to leave out, so $\binom{10}{8} = \binom{10}{2}$ .
$\binom{10}{2} = \dfrac{10 \times 9}{2 \times 1}$
$= 45$ , option D.