You are dealt a flush in the game of poker when you are dealt five cards of the same suit. If you are dealt a five-card hand, find the probability you will be dealt a heart flush.
Just continuing from the post above.... Classical probability - number of relevant events divided by total number of events: $\displaystyle \frac{ {13 \choose 5}}{{52 \choose 5}} $. One event is choosing 5 cards from a 52 cards deck. Relevant events are those where you ensure that all 5 cards will be of heart suit. So you isolate heart suited cards. From 13 of them you choose 5. There are $\displaystyle {13 \choose 5}$ ways to do that. Now total number of events is the number of ways to choose 5 from 52: $\displaystyle {52 \choose 5}$. Divide those two and you have your probability.