Answer
$19,600$ ways
Work Step by Step
The order in which the winning tickets are chosen is not important
(they yield the same prize whether first or third).
Combinations, ${}_{n}C_{r}=\displaystyle \frac{n!}{(n-r)!r!}$
${}_{50}C_{3}=\displaystyle \frac{50!}{(50-3)!3!}=\frac{50\times 49\times 48}{1\times 2\times 3}$
$=\displaystyle \frac{50\times 49\times 8}{1\times 1\times 1}=19,600$