Given the set of integers {1,...,n}, I would like to sample uniformly from the binom{n+k-1}{k} distinct multi-subsets of size k. Is there an efficient way of doing this?
For example, the set {1,2,3} has 6 multi-subsets of size 2. These are {1,2}, {2,3}, {1,3}, {1,1}, {2,2}, {3,3}.