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?

By stars and bars, the number of ways is C(51,4) = 249900.

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