There are three candidates running for math team president. The thirty members of the team can cast a vote for one canidate or they can choose to not vote. How many ways can the votes be distributed?
Let's use a Stars and Bars approach on this. There are 30 votes(stars) and 4 choices, but to get 4 catergories we only need 3 bars. In order to find where these bars would go, we can do 33C3 which is 5456.