Answer
The number of ways to select three city commissioners from a group of six candidates is 20.
Work Step by Step
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$
$\begin{align}
& {}_{6}{{C}_{3}}=\frac{6!}{\left( 6-3 \right)!3!} \\
& =\frac{6!}{3!\times 3!}
\end{align}$
$=20$
