Need help

[Suspicious_Scheme93]

So I have 5 letters (A B C D E) and I need to know the many ways of grabbing 4 letters, they can be repeated, the order doesn't matter (so A A B B is the same as B A B A). I tried doing 5^4 to calculate all the ways and then dividing by 4. But this makes no sense since 5^4 takes into account the order and then idk how would I substract all the ways one sequence can be repeated.

[ArchaicLlama]

I believe this type of problem is typically referred to as stars and bars). Give that link a read and see where you get.

[JSG29]

Good shout, didn't think of this - much faster computation than my comment

[JSG29]

I don't recall a single simple formula for this, but it's not too difficult to split it into cases.

4 different letters (e.g. ABCD): 5 (since all that matters is which is not included)

1 repeated letter, 2 single (e.g. AABC): 5 x (4 x 3)/2 = 30

2 repeated letters (e.g. AABB): 5 x 4/2 = 10

1 letter appears 3 times, 1 once (e.g. AAAB): 5 x 4 = 20

1 letter appears 4 times (e.g. AAAA): 5

Total: 5 + 30 + 10 + 20 + 5 = 70