  Markov categories, having tensors with copying and discarding, provide a
setting for categorical probability. This paper uses finite colimits and what
we call uniform states in such Markov categories to define a (fixed size)
multiset functor, with basic operations for sums and zips of multisets, and a
graded monad structure. Multisets can be used to represent both urns filled
with coloured balls and also draws of multiple balls from such urns. The main
contribution of this paper is the abstract definition of multinomial and
hypergeometric distributions on multisets, as draws. It is shown that these
operations interact appropriately with various operations on multisets.
