Suppose you want to make 500 draws, where you have 26 letters of the English alphabet in a bag. They come in equal quantities and their supply is unlimited, so that you could, for example, draw 500 "A's". How many different combinations are there for the number of these letters thus chosen?
It's hard for me to even formulate the question, and I realize the title is clumsy, so if someone can find better wording, please comment on it and I'll edit the post. But to give you an example, one combination would be 500 A's, another 498 A's, 2 B's, and yet another one, say, 467 A's, 23 C's and 10 D's.
This is not a homework question, but it was a related homework question I know how to solve that got me thinking about this. I tried to find a simple solution, but couldn't really find one, and to me the problem actually seems quite involved. Any thoughts on this?