L02_F10 - AMS 311: Introduction to Probability Spring...

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AMS 311: Introduction to Probability Spring Semester, 2010: Lecture 2 Chapter One: Combinatorial Analysis 1.2. The Basic Principle of Counting Basic Principle of Counting: Suppose that two experiments are to be performed. Then if experiment 1 can result in any one of m possible outcomes and if for each outcome of experiment 1 there are n possible outcomes of experiment 2, then together there are mn possible outcomes of the two experiments. Generalized Basic Principle of Counting: If r experiments that are to be performed are such that the first one may result in 1 n possible outcomes, and if for each of these 1 n possible outcomes there are 2 n possible outcomes of the second experiment, and if for each of the possible outcomes of the first two experiments there are 3 n possible outcomes of the third experiment, and if then there is a total of r n n n n × × × 3 2 1 possible outcomes of the r experiments. Remember that the generalized counting principle allows the set of objects from which
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L02_F10 - AMS 311: Introduction to Probability Spring...

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