# The Principle of Inclusion and Exclusion

• George E. Martin
Part of the Undergraduate Texts in Mathematics book series (UTM)

## Abstract

Let’s begin with some comments about Figure 2.1, which is on the next page. We are looking at properties of subsets A, B, C of some universal set that has t elements. The universal set in the figure is represented by the rectangles. For each set S, we let |S| denote the number of elements in S and say that |S| is the size of S. Looking at the top third of the figure, we see a trivial result that is tremendously important. Frequently it is much easier to count the elements in a set by first counting the elements not in the set. For example, counting the 5-letter words that have a vowel is very difficult without first counting the number of 5-letter words that have no vowel. The number of 5-letter words that have a vowel is 265 – 215.

## Keywords

Round Table Stirling Number Seating Arrangement Hardware Store Additional Male
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.