Combinatorics

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Unformatted text preview: –  Product rule, sum rule, Principal of Inclusion Exclusion (PIE) –  Applica5on of PIE: Number of onto func5ons •  Pigeonhole principle –  Generalized, probabilis5c forms •  •  •  •  Permuta5ons Combina/ons Binomial Coefficients Generaliza5ons –  Combina5ons with repe55ons, permuta5ons with indis5nguishable objects •  Algorithms –  Genera5ng combina5ons (1), permuta5ons (2) •  More Examples CSCE 235 Combinatorics 35 Combina5ons (1) •  Whereas permuta5ons consider order, combina5ons are used when order does not maxer •  Defini/on: A k- combina5on of elements of a set is an unordered selec5on of k elements from the set. (A combina5on is imply a subset of cardinality k) CSCE 235 Combinatorics 36 Combina5ons (2) •  Theorem: The number of k- combina5ons of a set of cardinality n with 0 ≤ k...
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This note was uploaded on 10/31/2013 for the course CSCE 235 taught by Professor Staff during the Spring '08 term at UNL.

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