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# L03_F10 - AMS 311 Lecture 3 Spring 2010 Generalized Basic...

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AMS 311: Lecture 3 Spring 2010 Generalized Basic Principle of Counting : If r that are to be performed are such that the first one may result in n 1 possible outcomes, and if for each of these n 1 possible outcomes there are n 2 possible outcomes of the second experiment, and if for each of the possible outcomes of the first two experiments there are n 3 possible outcomes of the third experiment, and if …, then there is a total of n 1 × n 2 × …× n r possible outcomes of the r experiments. The number of distinguishable permutations of n objects of k types, where 1 n are alike, 2 n are alike, , k n are alike, and k n n n n + + + = 2 1 is ! ! ! ! 2 1 k n n n n 1.4. Combinations Definition. An unordered arrangement of r objects from a set A containing n objects ( r # n ) is called an r -element combination of A , or a combination of the elements of A taken r at a time. There are n C r combinations of r elements chosen from n objects, where ! )! ( ! r r n n C r n - = Example. Consider a set of n antennas of which m are defective and n-m are functional and assume that all of the defectives and all of the functionals are considered indistinguishable. How many linear orderings are there in which no two defectives are

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