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Unformatted text preview: Chapter 3 Combinatorics 3.1 Permutations Many problems in probability theory require that we count the number of ways that a particular event can occur. For this, we study the topics of permutations and combinations. We consider permutations in this section and combinations in the next section. Before discussing permutations, it is useful to introduce a general counting tech- nique that will enable us to solve a variety of counting problems, including the problem of counting the number of possible permutations of n objects. Counting Problems Consider an experiment that takes place in several stages and is such that the number of outcomes m at the n th stage is independent of the outcomes of the previous stages. The number m may be different for different stages. We want to count the number of ways that the entire experiment can be carried out. Example 3.1 You are eating at ´ Emile’s restaurant and the waiter informs you that you have (a) two choices for appetizers: soup or juice; (b) three for the main...
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This note was uploaded on 09/15/2009 for the course SCF scf taught by Professor Scf during the Spring '09 term at Indian Institute Of Management, Ahmedabad.
- Spring '09