Answer
$50_{{C}{_{3}}}$ = 19600
Work Step by Step
Total number of people purchasing raffle ticket = 50
Number of winners = 3
To find the number of ways to select 3 winner out of 50, we use the formula $n_{{C}{_{r}}}$ = $\frac{n!}{(n - r)! . r!}$ because the prize for all three is the same, we don't need to arrange the prize.
The number of ways of selection = $50_{{C}{_{3}}}$ = $\frac{50!}{(50 - 3)! . 3!}$
= $\frac{50!}{47! . 3!}$
= $\frac{50\times49\times48\times47!}{47!. (3\times2\times1)}$
= $\frac{50\times49\times48}{3\times2\times1}$
= 19600
