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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. For each problem, we derive a formula that lets us determine the number of possible outcomes. The problems we study are: Counting assignments (Section ).

two houses, corresponding to the nine different pairs of letters, each letter chosen from R, G, and B. Similarly, for each of the nine assignments of colors to the first two houses, we may select a color for the third house in three possible ways. Thus, there are 9× 3 = 27 ways to paint the first three houses. Finally, each of these 27

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