One of our very first counting principles was the sum principle which says that the size of a union of disjoint sets is the sum of their sizes. Computing the size of overlapping sets requires, quite n...One of our very first counting principles was the sum principle which says that the size of a union of disjoint sets is the sum of their sizes. Computing the size of overlapping sets requires, quite naturally, information about how they overlap. Taking such information into account will allow us to develop a powerful extension of the sum principle known as the “principle of inclusion and exclusion.”
In this section, we explore the basic counting principles through a plethora of examples and exercises. One of our goals in these notes is to show how most counting problems can be recognized as count...In this section, we explore the basic counting principles through a plethora of examples and exercises. One of our goals in these notes is to show how most counting problems can be recognized as counting all or some of the elements of a set of standard mathematical objects. You may have noticed some standard mathematical words and phrases such as set, ordered pair, function, and so on creeping into the problems.