On Average Numbers of Identical (Microscopic) Objects in Their N_s ≥ 3 Possible (Spatial) States and with Probabilistic Transitions between Them in a System with a Constant Number of These (Microscopic) Objects

A system consisting of a constant number N of identical objects, each of which can be in one of N_s ≥ 3 states connected, by definition, by probabilistic relations, is analyzed. The values of these probabilities are determined, as well as the average numbers of the objects in the states and their minimum and maximum possible values, which determine the ranges of variation of these quantities. In particular, the results of this study can be used in the physics of microscopic objects (e.g., atoms) that also exist in hypothetic spaces with dimensions D > 3 (including the values of D = 5, 9 appearing in some models of the field theory). Apart from such a purely scientific value, this study is of the methodical interest as an illustration of basic concepts of the probability theory as applied to the problem under investigation with a possible application in combinatorics.