Answer
The number of ways to award the prize to three people out of 50 is $19,600$.
Work Step by Step
We know that:
${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$
So, from the information,
$\begin{align}
& n=50 \\
& r=3 \\
\end{align}$
Then, we have to find the number of combinations of 50 things taken 3 at a time:
$\begin{align}
& {}_{50}{{C}_{3}}=\frac{50!}{3!\left( 50-3 \right)!} \\
& =\frac{50!}{3!47!} \\
& =\frac{50\times 49\times \ldots \times 47!}{3!47!} \\
& =19,600
\end{align}$
Thus, the number of ways to award the prize to three people out of 50 is $19,600$.
