  The multiplicities of the decomposition of the product of an arbitrary number
$n$ of spin $s$ states into irreducible $SU(2)$ representations are computed.
Two complementary methods are presented, one based on random walks in
representation space and another based on the partition function of the system
in the presence of a magnetic field. The large-$n$ scaling limit of these
multiplicities is derived, including nonperturbative corrections, and related
to semiclassical features of the system. A physical application of these
results to ferromagnetism is explicitly worked out. Generalizations involving
several types of spins, as well as spin distributions, are also presented. The
corresponding problem for (anti-)symmetric composition of spins is also
considered and shown to obey remarkable duality and bosonization relations and
exhibit qualitatively different large-$n$ scaling properties.
