Combinatorics

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Unformatted text preview: fficients Generaliza5ons –  Combina5ons with repe55ons, permuta5ons with indis5nguishable objects •  Algorithms –  Genera5ng combina5ons (1), permuta5ons (2) •  More Examples CSCE 235 Combinatorics 42 Binomial Coefficients (1) •  The number of r- combina5ons is also called the binomial coefficient •  The binomial coefficients are the coefficients in the expansion of the expression, (mul5variate polynomial), (x+y)n •  A binomial is a sum of two terms CSCE 235 Combinatorics 43 Binomial Coefficients (2) •  Theorem: Binomial Theorem Let x, y, be variables and let n be a nonnega5ve integer. Then Expanding the summa5on we have Example CSCE 235 Combinatorics 44 Binomial Coefficients: Example •  What is the coefficient of the term x8y12 in the expansion of (3x+4y)20? –  By the binomial theorem, we have –...
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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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