In this chapter, we look at techniques for answering the question "how many?" without having to count each item, one by one. Numbers that are answers to the question "how many?" are called cardinal numbers. The study of the properties of cardinal numbers is one of the oldest and most fascinating branches of mathematics. Questions about cardinal numbers that have been worked on for thousands of years remain unanswered to this day.

1.1 One, two, three, ...

1.2 Some counting problems and estimates

1.3 A fundamental counting principle

1.4 Permutations

1.5 Two complications

1.6 Combinations