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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 4 candidates. How many different possible vote totals are there?

 Aug 19, 2020
 #1
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By stars and bars, the number of ways is C(51,4) = 249900.

 Aug 19, 2020
 #2
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I also am using stars and bars method.

 

53C3 =   23426 ways

 

We have 50 people divide by 3 bars.  That will create 4 groups of people

Now we have to decide where the 3 bars go.

Hence 53C3

 Aug 19, 2020

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