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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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 Spring '09

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