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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!

Sep 3, 2020
edited by Guest  Sep 3, 2020

#1
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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.

Sep 3, 2020
#3
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Thanks for helping out Mathulator. Unfortunately, $$4^{50}$$ is incorrect.

Guest Sep 4, 2020