Precalculus (6th Edition) Blitzer

The order in which the city commissioners are selected does not matter. Thus, this is a problem of selecting 3 people from a group of 6 candidates. We need to find the number of combinations of 6 things taken 3 at a time. Apply the formula, ${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$ Where $n=6,r=3$ \begin{align} & {}_{6}{{C}_{3}}=\frac{6!}{\left( 6-3 \right)!3!} \\ & =\frac{6!}{3!\times 3!} \end{align} $=20$