## Thinking Mathematically (6th Edition)

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