ABSTRACT
One of the basic purposes of combinatorics is enumeration, and we have seen many ways to enumerate arrangements of objects. The binomial coefficients enumerate ways of choosing a subset of distinct objects from a set; factorials and permutation numbers enumerate ways of choosing an ordered subset; and so on. In general, we distinguish several classes of problems involving enumeration of arrangements of objects. The objects may be distinct or identical; the arrangements may be considered distinct when order is changed (order important) or not (order unimportant); and we may distinguish amongst the classes in which they are arranged, or not. Also, we may ask whether repetition is allowed, or not (and if so, whether the repetition may be unlimited); whether all objects must be arranged; and whether all the classes into which they are to be arranged must receive at least one object.
