ABSTRACT
Explaining what combinatorics is about may be simple since it deals with objects and techniques that are quite familiar to most people. Yet, combinatorics is not easy to define precisely. At the fundamental level, combinatorics deals with the questions related to counting the number of elements in a given set; a bit more precisely, combinatorics deals with discrete structures. Moreover, beyond its object of study, combinatorics can be characterized by its methods. Typically, by the combinatorial method we mean a relatively basic—but, perhaps, surprisingly deep and far-reaching—argument using some relatively elementary tools, rather than the application of sophisticated and elaborately developed machinery. That is what makes combinatorics so highly applicable. Enumeration—or, simply, counting—is probably one of the earliest intellectual pursuits, and it is a ubiquitous task in everyday life. The principles of enumeration are also what several branches of mathematics are based on, especially probability theory and statistics.
