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Combinatorics and Probability - Stanford University

CHAPTER 4.. Combinatorics .. and Probability In computer science we frequently need to count things and measure the likelihood of events. The science of counting is captured by a branch of mathematics called Combinatorics . The concepts that surround attempts to measure the likelihood of events are embodied in a field called Probability theory. This chapter introduces the rudiments of these two fields. We shall learn how to answer questions such as how many execution paths are there in a program, or what is the likelihood of occurrence of a given path? .. What This Chapter Is About We shall study Combinatorics , or counting, by presenting a sequence of increas- ingly more complex situations, each of which is represented by a simple paradigm problem.

ingly more complex situations, each of which is represented by a simple paradigm problem. For each problem, we derive a formula that lets us determine the number of possible outcomes. The problems we study are: Counting assignments (Section 4.2). The paradigm problem is how many ways can we paint a row of n houses, each in any of k colors.

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