This article in Wikipedia may help.
multiset:= consists of a set S, together w/ positive integers m_x for every x element of S.
Problem: find the number of k-element multisets with elements in a given set Y. Size of Y =n
The soln our prof showed us involved "flags and flagpoles." The heuristic behind this is that the distribution of {1,....,k} "flags" into n-labeled flagpoles can be mapped to a unique multiset. Each multiset corresponds to a k! distributions of flags on flagpoles. I am not sure how he derived the formula for calculating the distributions of [k] into n-labeled flags.
n * (n+1) * (n+2)....(n+k-1)
This has been driving me crazy all morning guys. Please help!