At an introductory level, combinatorics is usually considered as a branch of discrete mathematics in which the main problem is that of counting the number of ways of arranging or choosing objects from a finite set according to some simple specified rules. Thus the crux of the problem, at the beginning stage at least, is mainly that of enumeration. But if the prescribed rules and constraints become complicated the question to ask naturally is whether an arrangement satisfying the given requirements exists in the first place; if so, in the subsequent analysis one investigates the methods of constructing such arrangements. In some cases these arrangements also have to meet certain optimality criteria, in which case we seek an optimal solution of the problem. A typical statement in some of these optimal situations will assert that the minimum for one kind of a selection will correspond to the maximum for another kind, yielding a max min theorem. Thus in a wider sense, combinatorics deals with the enumeration, existence, analysis, and optimization of discrete structures.