  A packing of subsets $\mathcal S_1,..., \mathcal S_n$ in a group $G$ is a
sequence $(g_1,...,g_n)$ such that $g_1\mathcal S_1,...,g_n\mathcal S_n$ are
disjoint subsets of $G$. We give a formula for the number of packings if the
group $G$ is finite and if the subsets $\mathcal S_1,...,\mathcal S_n$ satisfy
a genericity condition. This formula can be seen as a generalization of the
falling factorials which encode the number of packings in the case where all
the sets $\mathcal S_i$ are singletons.
