Combinatorial Math-ECO6416

Combinatorial Math-ECO6416 - Combinatorial Math: How to...

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Combinatorial Math: How to Count Without Counting Many disciplines and sciences require the answer to the question: How Many? In finite probability theory we need to know how many outcomes there would be for a particular event, and we need to know the total number of outcomes in the sample space. Combinatorics , also referred to as Combinatorial Mathematics , is the field of mathematics concerned with problems of selection, arrangement, and operation within a finite or discrete system. Its objective is: How to count without counting. Therefore, One of the basic problems of combinatorics is to determine the number of possible configurations of objects of a given type. You may ask, why combinatorics? If a sample spaces contains a finite set of outcomes, determining the probability of an event often is a counting problem. But often the numbers are just too large to count in the 1, 2, 3, 4 ordinary ways. A Fundamental Result: If an operation consists of two steps, of which the first can be done in n1ways and for each of these the second can be done in n2 ways, then the entire operation can be done in a total of n1× n2 ways. This simple rule can be generalized as follow: If an operation consists of k steps, of which the first can be done in n1 ways and for each of these the second step can be done in n2 ways, for each of these the third step can be done in n3 ways and so forth, then the whole operation can be done in n1 × n2 × n3 × n4 ×. . × nk ways.
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Combinatorial Math-ECO6416 - Combinatorial Math: How to...

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