  We give explicit expressions for the q-multinomial generalizations of the
q-binomials and Andrews' and Baxter's q-trinomials. We show that the
configuration sums for the generalized RSOS models in regime III studied by
Date et al. can be expressed in terms of these multinomials. This generalizes
the work of ABF and AB where configuration sums of statistical mechanical
models have been expressed in terms of binomial and trinomial coefficients.
These RSOS configuration sums yield the branching functions for the
$\widehat{su}(2)_{M}\times \widehat{su}(2)_{N}/\widehat{su}(2)_{M+N}$ coset
models. The representation in terms of multinomials gives Rocha-Caridi like
formulas whereas the representation of Date et al. gives a double sum
representation for the branching functions.
