Generalization of the classical scheme of allocating particles into cells by sets implies extending its conditions to allow different sizes of sets. This allocation scheme is studied separately for cases without empty cells and by selected cells. The study is carried out by the enumeration method based on the construction and analysis of an iterative random process of direct non-repetitive numbered enumeration of its outcomes in the pre-asymptotic region of parameter change in the following directions: solving the numbering problem in direct and inverse formulations which consist in finding one-to-one correspondence between the numbers and types of outcomes of the scheme, determining the probabilistic distribution of the number of empty cells and on the set of outcomes of the scheme according to the introduced probabilities of iterative transitions of the process of their enumeration and developing a procedure for their modeling.