We consider a scheme C of allocating r = r(k) indistinguishable particles to n distinguishable cells until the occurrence of the event Ak, when for the first time there are k (k r) non-empty cells. The pre-asymptotic analysis of the scheme is carried out by an original enumerative method (EM) along the following lines: nonrepetitive enumeration and determination of the number of its outcomes, solutions to the numbering problem offinding one-to-one correspondence between the numbers and types of the scheme’s outcomes, determining the probability distribution on the set of its outcomes, and a procedure for their modeling is proposed. For all other paired qualities according to distinguishability of the elements (cells and particles) that make up the scheme, a method is proposed for recalculating the initial results of the C scheme.