Probability raffle question There is a raffle with prizes for first, second and third. There are $50$ tickets. A teacher buys $5$. What is the probability that; $1$) wins first prize. $2$) wins at least one prize.

$1$)The answer is $\frac{5}{50}=\frac{1}{10}$.

$2$)The second problem is harder, so I'll explain. We can first find the probability for not winning any prize. the probability for not winning first prize is $1-\frac{5}{50}=\frac{9}{10}$, not winning second prize is $1-\frac{5}{50}=\frac{9}{10}$, not winning third prize is $1-\frac{5}{50}=\frac{9}{10}$. So the probability for not winning any prize is $\big(\frac{9}{10}\big)^3=\frac{729}{1000}$. So the probability for winning at least one prize is $1-\frac{729}{1000}=\frac{271}{1000}$.