Answer
$50_{{P}{_{3}}}$ = 117,600
Work Step by Step
This problem has the case of permutation thus we use the formula $n_{{P}{_{r}}}$ = $\frac{n!}{(n - r)!}$ because we have to choose 3 different prizes and distribute them in an order.
We have to choose and distribute 3 prizes out of 50 then the ways prize be awarded = $50_{{P}{_{3}}}$ = $\frac{50!}{(50 - 3)!}$
= $\frac{50\times49\times48\times47!}{47! }$ = 117,600
