Collisional processes leading to the formation of nanoparticles in a laser-ablated plume are numerically simulated with the aid of an atomistic-level model based on direct simulation Monte Carlo (DSMC) method. The formation of nanoparticles in nanosecond laser ablation of a mono-atomic target is investigated in the presence of an inert background gas. The DSMC procedure is modified in order to account for numerous plume species and to describe several reactions (i.e., recombination/dissociation, sticking, evaporation) taking place in the plume and affecting the size and spatial distribution of the produced nanoclusters. Calculation results allow us to visualize the nanoparticles and to correlate their space distributions with plume dynamics. In addition, cluster size distributions are investigated at different pressures. The effects of the background gas on cluster formation within the plume are furthermore shown.