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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 •
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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.
 Spring '08
 STAFF

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