Calculating the minimal number of homogeneous objects to represent a plurality in a heterogeneous system of objects

Formulae for calculating the minimal number of homogeneous objects to constitute a plurality of objects within a finite heterogeneous system are presented. Such a system is searched for among all systems that can be formed by groups of available types of homogeneous objects and consist of one and the same total number of objects grouped into one and the same number of groups of homogeneous objects.