The answer is \(\boxed{4^{50}}\), and here's why.
We have 50 people, and four people to vote for. Let's see how many possibilities for a single person. The person can vote for person A, B, C, or D, thus meaning there are four options for a single person. Remember that one person's vote does not affect another; for example if thirty-nine people voted for person C, it does not make the fortieth person any more likely to vote for person C, all probabilities are independent.
So we have \(4^1\) for the first person, because there is one person voting. But each time we have more people vote, the options increase. If we had two people voting, there would be \(4\cdot4\) options or \(4^2\). This pattern goes on for every single vote, meaning that by the end, we will have \(\boxed{4^{50}}\) options.
