lec16-counting - EECS 203 Winter 2007 Discrete Mathematics...

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EECS 203, Winter 2007 Discrete Mathematics Lecture 16 Basic counting; Inclusion-Exclusion Principle; Pigeonhole Principle March 6 Reading: Rosen [5.1, 5.2] March 6 Basic counting; Inclusion-Exclusion Principle; Pigeonhole Principle, Page 1
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16.1 Basic counting principles Two simple formulas If A = A 1 × A 2 × · · · A m , then | A | = Π m i =1 | A i | . If A = A 1 A 2 ∪ · · · ∪ A m and A i A j = ϕ , for all i = j , then | A | = m i =1 | A i | . Use them to do counting: The Product Rule: if a task can be decomposed into m steps, each step has n i options, i = 1 , ..., m then the total number of options for completing the task is Π m i =1 n i . The Sum Rule: if a task can be accomplished in one of n 1 ways, or, one of n 2 ways, or, ..., one of n m ways, and no pair of those ways are the same, then there are in total n 1 + · · · + n m March 6 Basic counting; Inclusion-Exclusion Principle; Pigeonhole Principle, Page 2
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16.1 Basic counting principles ways to accomplish the task.
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  • Winter '07
  • YaoyunShi
  • Combinatorics, Natural number, Finite set, Ramsey's theorem

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