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(i.e., with replacement) but disregarding different orderings (e.g. {2,1,2} = {1,2,2}). Associate an index to each element of S and think of the elements of S as types of objects, then we can let denote the number of elements of type i in a multisubset. The number of multisubsets of size k is then the number of nonnegative integer (so allowing zero) solutions of the Diophantine equation:

If S has n elements, the number of such k-multisubsets is denoted by

a notation that is analogous

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