Lecture3 - Combinations 9/29/2005 Problem: A certain state...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Combinations 9/29/2005
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Problem: A certain state has license plates showing three numbers and three letters. How many different license plates are possible 1. if the numbers must come before the letters? 2. if there is no restriction on where the letters and numbers appear? 1
Background image of page 2
As I was going to St. Ives, I met a man with seven wives, Each wife had seven sacks, Each sack had seven cats, Each cat had seven kits. Kits, cats, sacks and wives, How many were going to St. Ives? 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Binomial Coefficients Definition. The number of distinct subsets with j elements that can be chosen from a set with n elements is denoted by ( n j ) . The number ( n j ) is called a binomial coefficient . 3
Background image of page 4
Recurrence Relation Theorem. For integers n and j , with 0 < j < n , the binomial coefficients satisfy: ± n j = ± n - 1 j + ± n - 1 j - 1 . 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Pascal’s triangle n = 0 1 10 1 10 45 120 210 252 210 120 45 10 1 9 1 9 36 84 126 126 84 36 9 1 8 1 8 28 56 70 56 28 8 1 7 1 7 21 35 35 21 7 1 6 1 6 15 20 15 6 1 5 1 5 10 10 5 1 4 1 4 6 4 1 3 1 3 3 1 2 1 2 1 1 1 1 j = 0 1 2 3 4 5 6 7 8 9 10 5
Background image of page 6
Theorem. The binomial coefficients are given by the formula ± n j = ( n ) j j !
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 19

Lecture3 - Combinations 9/29/2005 Problem: A certain state...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online