0 1010 1 1 1001 0 1 0010 0 0 0100 1 0001

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 –...
View Full Document

This note was uploaded on 10/31/2013 for the course CSCE 235 taught by Professor Staff during the Spring '08 term at UNL.

Ask a homework question - tutors are online