Answer
The number of ways to select 6 people out of 13 people to test the effectiveness of the experiment is $1,716$.
Work Step by Step
We know that:
${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$
So, from the information,
$\begin{align}
& n=13 \\
& r=6
\end{align}$
Then, we have to find the number of combinations of 13 things taken 6 at a time:
$\begin{align}
& {}_{13}{{C}_{6}}=\frac{13!}{6!\left( 13-6 \right)!} \\
& =\frac{13!}{6!7!} \\
& =\frac{13\times 12\times 11\times 10\times 9\times 8\times 7!}{6!\times 7!} \\
& =1,716
\end{align}$