Answer
The number of way to select and distribute prize = $50_{{C}{_{3}}}$ = 117,600
Work Step by Step
Total number of people purchasing raffle tickets = 50
Number of winners = 3
To find the number of ways to select winner and distribute prize we use the formula $n_{{P}{_{r}}}$ = $\frac{n!}{(n - r)!}$
The number of ways to select and distribute prize = $50_{{C}{_{3}}}$ = $\frac{50!}{(50 - 3)!}$
= $\frac{50!}{47! }$
= $\frac{50\times49\times48\times47!}{47!}$
= $50\times49\times48$
= 117,600
