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(51,5) = 2349060.
What di did is thought about the 50 people (stars) and they had to be separated in 4 groups.
You need 3 bars to do this.
ex ***|*****|******|** here you can see that these stars (not 50) are separated into 4 groups using just 3 bars.
So altogether you have 50 stars place 3 bars and you need to know how many places the set of 3 bars can go.
That is 53C3 possibilities.