A set of methods for limiting the complete enumeration of the number of combinations Ckn for 1 ≤ k ≤ n is proposed. The proposed methods can be used in combinatorial algorithms for calculating subsets of the original set. They are applicable if the calculation of subsets is carried out using a selection function with certain properties. An example of using an algorithm to calculate the set of minimal sections of a graph is considered. It is shown that these methods can be used to solve a number of different NP-complete problems. The results of numerical experiments are presented.