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Unformatted text preview: hout labels, such as IILN IL corresponds to 3! × 2 = 12 orderings
with labels, because there are 3! ways to label the three I ’s, and for each of those, there are two
ways to label the L’s. Hence, there are 720/12 = 60 ways to form a sequence of six letters, using
three identical I ’s, two identical L’s, and one N. Principle of Over Counting The above two examples illustrate the principle of over counting,
which can be stated as follows: For an integer K ≥ 1, if each element of a set is counted K times,
then the number of elements in the set is the total count divided by K.
Example 1.3.5 Suppose nine basketball players are labeled by the letters A, B, C, D, E, F, G, H,
and I. A lineup is a subset consisting of ﬁve players. For example, {A, B, D, E, H } is a possible lineup. The order of the letters in the lineup is not relevant. That is, {A, B, D, E, H } and
{A, B, E, D, H } are considered to be the same. So how many distinct lineups are there?
Solution: If the order did matter, the prob...
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 Spring '08
 Zahrn
 The Land

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