Combinatorics

Combinatorics

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Unformatted text preview: coin tosses, how many ways can 3 heads and 7 tails come up? –  The number of ways of choosing 3 heads out of 10 coin tosses is –  It is the same as choosing 7 tails out of 10 coin tosses –  … which illustrates the corollary CSCE 235 Combinatorics 40 Combina5ons: Example C •  How many commixees of 5 people can be chosen from 20 men and 12 women –  If exactly 3men must be on each commixee? –  If at least 4 women must be on each commixee? •  If exactly three men must be on each commiEee? –  We must choose 3 men and 2 women. The choices are not mutually exclusive, we use the product rule •  If at least 4 women must be on each commiEee? –  We consider 2 cases: 4 women are chosen and 5 women are chosen. Theses choices are mutually exclusive, we use the addi5on rule: CSCE 235 Combinatorics 41 Outline •  Introduc5on •  Coun5ng: –  Product rule, sum rule, Principal of Inclusion Exclusion (PIE) –  Applica5on of PIE: Number of onto func5ons •  Pigeonhole principle –  Generalized, probabilis5c forms •  •  •  •  Permuta5ons Combina5ons Binomial Coe...
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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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