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Combinatorics - Harvard University

Chapter 1. Combinatorics Copyright 2009 by David Morin, (Version 4, August 30, 2009). This file contains the first three chapters (plus some appendices) of a potential book on probability and Statistics. It does not assume knowledge of calculus. The first three chapters are titled Com- binatorics, probability , and Distributions. And Appendix B gives a nice little introduction to the natural logarithm, e. Future chapters on statistics will be added in the summer of 2010. Combinatorics is the study of how to count things. By things we mean the various combinations, permutations, subgroups, etc., that can be formed from a given set of objects or events. For example, how many different committees of three people can be chosen from five people? How many different full-house hands are there in poker? How many different outcomes are possible if you flip a coin four times? Knowing how to count such things is critical for an understanding of probability , because when calculating the probability of a given event, we invariably need to count the number of ways that this event can happen.

a probability once you’ve counted the relevant things, so the bulk of the work we’ll need to do will be in the present chapter. 1.1 Factorials Before getting into the discussion of actual combinatorics, we’ll flrst need to look at a certain quantity that comes up again and again. This quantity is called the factorial. We’ll see

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