Combinatorics

# Now say that only one event can occur not both in this

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Unformatted text preview: usive then the number of ways of both events occurring is n1+ n2 CSCE 235 Combinatorics 5 Sum Rule (2) •  There is a natural generaliza5on to any sequence of m tasks; namely the number of ways m mutually exclusive events can occur n1 + n2 + … + nm- 1 + nm •  We can give another formula5on in terms of sets. Let A1, A2, …, Am be pairwise disjoint sets. Then |A1 ∪ A2 ∪ … ∪ Am | = |A1| ∪ |A2| ∪ … ∪ |Am| (In fact, this is a special case of the general Principal of Inclusion- Exclusion (PIE)) CSCE 235 Combinatorics 6 Principle of Inclusion- Exclusion (PIE) •  Say there are two events, e1 and e2, for which there are n1 and n2 possible outcomes respec5vely. •  Now, say that only one event can occur, not both •  In this situa5on, we cannot apply the...
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