If there are $200$ students in the library, how many ways are there for them to be split among the floors of the library if there are $6$ floors? Need help studying for an exam.
Practice Question:
If there are $200$ students in the library, how many ways are there for them to be split among the floors of the library if there are $6$ floors?
Hint: The students can not be told apart (they are indistinguishable).
The answer must be in terms of $P(n,r), C(n,r)$, powers, or combinations of these. The answers do not have to be calculated.

I'm too new here to comment on @Sivaram's answer, but I believe it to be correct and well explained. For further reference see Stanley's "Twelvefold Way" in Combinatorics at either [1] or the Wikipedia page.
[1] http://mathsci.kaist.ac.kr/~drake/pdf/twelvefold-way.pdf
