Multiplicity distributions, the dependence on $n$ of ${\psi }_n=\frac{{\sigma }_n}{\sigma }$, are discussed. Within the framework of the Amati-Fubini-Stanghellini model, a cluster expansion for the moments of ${\psi }_n$ is derived. This same expansion is then derived as a consequence of asymptotic dominance of inclusive reactions by an isolated, factorizable Regge pole. Such an expansion furnishes a systematic way of describing the shape of ${\psi }_n$. It is argued that a Poisson distribution for multiple particle production can not be expected to occur, even for very high energies.

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