Answer
The number of ways to select 6 people out of 14 standbys are $3003$
Work Step by Step
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.
