By means of a constrained canonical-ensemble Monte Carlo technique the equilibrium physical cluster distribution {n(ij)} in a supersaturated vapor mixture is computed. From this the intensive Gibbs free energy of ij-cluster formation DeltaG(ij) is obtained via the relation n(ij)=Ne-ij(-DeltaG)/k(B)T, where N is the number of molecules in the system, T is temperature, and k(B) is the Boltzmann constant. The saddle point on the free energy surface DeltaG(ij) versus i and j provides a measure of the activation barrier to nucleation DeltaG*. A statistical mechanical formula of DeltaG(ij) is derived based on the physical-cluster theory of nucleation, and from which a molecular interpretation of DeltaG(ij) is given. We applied the Monte Carlo method to investigate the mutual enhancement of nucleation in a binary model system which is composed of spherical Lennard-Jones monomers and rigid Lennard-Jones dimers consisting of a monophilic atom and a monophobic atom. This model system bears some qualitative similarity to the partially miscible water/higher alcohol systems in which the mutual enhancement of nucleation has been observed experimentally. The simulation confirms the existence of mutual enhancement of nucleation in monomer-rich vapors, as originally predicted by Napari and Laaksonen from a density-functional theory [Napari and Laaksonen, Phys. Rev. Lett. 84, 2184 (2000)]. The nucleation enhancement is also seen in dimer-rich vapors at high supersaturations.