The article studies the schemes of particle allocation to cells in indistinguishable (scheme A) and distinguishable (scheme B) groups with the outcomes of achieveming a given minimum cell filling level. The schemes are analyzed by the enumerative method based on the construction of an iterative random process of direct non-repetitive numbered enumeration of their outcomes in the pre asymptotic region of parameter change along the following lines: enumeration of outcomes and finding their number, solving the enumeration problem in direct and inverse formulations to establish one-to-one correspondence between the numbers and types of outcomes of the scheme, determining the probability distribution on the set of outcomes based on given probabilities of iterative transitions of the process of their enumeration, and developing a procedure for their modeling.