  We give a lightweight alternative construction of Jacobs's distributive law
for multisets and distributions that does not involve any combinatorics. We
first give a distributive law for lists and distributions, then apply a general
theorem on 2-categories that allows properties of lists to be transferred
automatically to multisets. The theorem states that equations between 2-cells
are preserved by epic 2-natural transformations. In our application, the
appropriate epic 2-natural transformation is defined in terms of the Parikh
map, familiar from formal language theory, that takes a list to its multiset of
elements.
