If there are n1 ways of doing the rst task and n2 ways

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Unformatted text preview: 5ons with indis5nguishable objects •  Algorithms –  Genera5ng combina5ons (1), permuta5ons (2) •  More Examples CSCE 235 Combinatorics 3 Product Rule •  If two events are not mutually exclusive (that is we do them separately), then we apply the product rule •  Theorem: Product Rule Suppose a procedure can be accomplished with two disjoint subtasks. If there are –  n1 ways of doing the first task and –  n2 ways of doing the second task, then there are n1.n2 ways of doing the overall procedure CSCE 235 Combinatorics 4 Sum Rule (1) •  If two events are mutually exclusive, that is, they cannot be done at the same 5me, then we must apply the sum rule •  Theorem: Sum Rule. If –  an event e1 can be done in n1 ways, –  an event e2 can be done in n2 ways, and –  e1 and e2 are mutually excl...
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