The recursive techniques developed by Mekjian and collaborators for exact c
alculations of canonical partition functions of fragmenting systems are ext
ended to allow the determination of fragment multiplicity distributions. Th
e fragment multiplicity distribution is shown to become strongly super-Pois
sonian at the critical temperature. This behavior is shown to be highly sen
sitive to Coulomb effects and to whether energy is strictly conserved (the
microcanonical ensemble). Additionally, a method is presented for generatin
g events from the partition functions, which also permits the inclusion of
hard-sphere interactions between fragments.