Let C be a collection of objects, characterized by the set A= {a1,⋯,an} of binary attributes. We consider problems of the following type: given an object-characterization table, it is to check if there exists a subset M in C of a given size, such that each attribute of A is satisfied by a given number of objects in M. Additional restriction may be applied such as - the number of matches of each object in M is limited. In this paper we investigate particular cases of the general problem, and consider approximation solutions by means of binary classification trees.