Thermodynamical properties of nuclear matter undergoing multifragmentation
are studied within a simplified version of the statistical model. An exact
analytical solution has been found for the grand canonical ensemble. Exclud
ed volume effects are taken into account in the thermodynamically self-cons
istent way. In the thermodynamic limit the model exhibits a first order liq
uid-gas phase transition with specific mixed phase properties. An extension
of the model including the Fisher's term is also studied. The possibility
of the second order phase transition at or above the critical point is demo
nstrated. The fragment mass distributions in different regions of the phase
diagram are discussed.