Combinatorics

# If at least 4 women must be on each commixee if

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Unformatted text preview: –  By the pigeonhole principle: 400 empty seats in 30 buses, one must have ⎡ྎ400/30 ⎤ྏ = 14 empty seats •  One of the buses will carry at least 67 passengers –  By the pigeonhole principle: 2000 passengers in 30 buses, one must have ⎡ྎ2000/30 ⎤ྏ = 67 passengers CSCE 235 Combinatorics 26 Outline •  Introduc5on •  Coun5ng: –  Product rule, sum rule, Principal of Inclusion Exclusion (PIE) –  Applica5on of PIE: Number of onto func5ons •  Pigeonhole principle –  Generalized, probabilis5c forms •  •  •  •  Permuta/ons Combina5ons Binomial Coeﬃcients Generaliza5ons –  Combina5ons with repe55ons, permuta5ons with indis5nguishable objects •  Algorithms –  Genera5ng combina5ons (1), permuta5ons (2) •  More Examples CSCE 235 Combinatorics 27 Permuta5ons •  A permuta5on of a set of dis5nct objects is an ordered arrangement of these objects. •  An ordered arrangement of r elements of a set of n elements is call...
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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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