# lec0109 - Counting Although counting seems to be a simple...

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Counting Although counting seems to be a simple straightforward task, many counting questions end up being quite counterintuitive. The study of discrete mathematics focuses on discrete quantities, namely the integers. Thus, the first topic of this course will be counting. A couple fairly intuitive rules, the sum and product rules, will first be introduced. Using these, we will derive some fairly interesting results and show how to tackle more difficult counting problems. One of the things to keep in mind here is that depending on HOW you view a counting problem, it could be quite easy or extremely difficult. One should not be discouraged if their initial approach is foiled or seems too difficult. Often times, different approaches to the same problem will eventually yield a fairly simple solution. Sum Rule If a first task can be performed in m ways, while a second task can be performed in n ways, and the two tasks cannot be performed simultaneously, then performing either task can be done in m+n ways. This is the book definition. Since most counting questions do

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## This document was uploaded on 07/14/2011.

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lec0109 - Counting Although counting seems to be a simple...

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