Precalculus (6th Edition) Blitzer

The number of ways to select 6 people out of 14 standbys are $3003$
We know that: ${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$ From the information, \begin{align} & n=14 \\ & r=6 \\ \end{align} Then to find the number of combinations of 14 things taken 6 at a time, apply the above formula: \begin{align} & {}_{14}{{C}_{6}}=\frac{14!}{6!\left( 14-6 \right)!} \\ & =\frac{14!}{6!8!} \\ & =\frac{14\times 13\times 12\times 11\times 10\times 9\times 8!}{\left( 8! \right)\times 6\times 5\times 4\times 3\times 2\times 1} \\ & =3003 \end{align} Thus, there are $3003$ ways to select 6 people out of 14 standbys.