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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?

2 CHAPTER 1. COMBINATORICS factorial," and it is denoted by the shorthand notation, \N!".1 For the flrst few integers, we have: 1! = 1 2! = 1¢2 = 2 3! = 1¢2¢3 = 6 4! = 1¢2¢3¢4 = 24 5! = 1¢2¢3¢4¢5 = 120 6! = 1¢2¢3¢4¢5¢6 = 720 (1.1) As N increases, N! gets very big very fast.For example, 10! = 3;628;800, and 20! … 2:43 ¢ 1018.In Chapter 3 we’ll make good use of an ...

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