Answer
$50_{{C}{_{3}}}$ = 19600
Work Step by Step
This problem has the case of combination only 3 prizes are the same and no need to arrange them, thus we use the formula $n_{{C}{_{r}}}$ = $\frac{n!}{(n - r)!. r!}$ because we have to choose 3 same prizes.
We have to choose and distribute 3 same prizes out of 50, then the ways the prizes are to be awarded = $50_{{C}{_{3}}}$ = $\frac{50!}{(50 - 3)!.3!}$
= $\frac{50\times49\times48\times47!}{47!.3\times2\times1 }$ = 19600
