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# Combinatorics

## What Is Combinatorics

Combinatorics is the mathematical study of the ways that groups of objects, e.g. students or coins, can be counted and organized. In the first two chapters, we focus on one of combinatoric's central concepts – counting methods. Counting may seem like a pretty trivial subject. Most of us learn to do it from a young age. When you look past the basics, however, there are plenty of no-trivial questions that we can ask like, “How many ways can you be dealt two of a kind in a poker hand?” or “How many different computer IP addresses are for connecting to the Internet?” In the last chapter, we switch directions and discuss the basics of sequences and series. The connection between sequences and series and combinatorics is a little tenuous but the idea of ordering a list of numbers and establishing a relationship between two sets will be important for students who want to learn more about the subject.

## Our Approach

Like many of White Crane Education's books, this one's focus is on practical calculation methods. However, we also try to explain the reasoning behind the methods and show how many of the formulas are derived. In that way, this book is part of a transition from the world of introductory mathematics where the focus is on doing calculations to a more advanced view where understanding why is as important as understanding how. The Analysis questions at the end of each section encourage students to take on this different approach by asking more probing questions that require a more abstract level of thinking.