A certain club has 50 people, and 4 members are running for president. Each club member votes for one of the candidates. How many different possible vote totals are there?

I know this question has been posted more than once, but they were all wrong, so can I get help from someone who is confident they have the right answer? Thank you!

Guest Sep 3, 2020

edited by
Guest
Sep 3, 2020

#1**+1 **

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.

Mathulator Sep 3, 2020