Discrete Math - Permute letters question

Question

How many ways are there to permute the letters in HAPPY?

Answer 1

Imagine the 2 P's were distinguishable. That would make the problem simple, the answer being 5! = 120.

However, if we need to account for how many times we overcounted because the P's are indistinguishable. In this case it is 2!, the number of permutations of "PP".

Thus our solution is 5!/2! = 60.

Similarly if you were to count the permutations of HAPPPY, the solution would be 5!/3! = 20.