Combinatorics

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Unformatted text preview: be the set of candies, |A|=6 –  Let B be the set of children, |B|=3 –  The problem becomes “find the number of surjec5ve mappings from A to B” (because each child must receive at least one candy) •  Thus the number of ways is thus (m=6, n=3) CSCE 235 Combinatorics 17 Outline •  Introduc5on •  Coun5ng: –  Product rule, sum rule, Principal of Inclusion Exclusion (PIE) –  Applica5on of PIE: Number of onto func5ons •  Pigeonhole principle –  Generalized, probabilis/c forms •  •  •  •  Permuta5ons Combina5ons Binomial Coefficients Generaliza5ons –  Combina5ons with repe55ons, permuta5ons with indis5nguishable objects •  Algorithms –  Genera5ng combina5ons (1), permuta5ons (2) •  More Examples CSCE 235 Combinatorics 18 Pigeonhole Principle (1) •  If there are more pigeons than there are roots (pigeonholes), for at least one...
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