Permutations Fundamental Principle of Counting If one task

  • Slides: 8
Download presentation
Permutations

Permutations

Fundamental Principle of Counting: If one task can be done x number of ways

Fundamental Principle of Counting: If one task can be done x number of ways and another task can be done y number of ways; then the total number of ways in which these tasks can be completed together is the PRODUCT. Example: A club consists of 15 boys and 20 girls. They wish to elect a girl as president and a boy as Vice President. They also wish to elect a Secretary and a Treasure who may be either a boy or girl. (# choices for Pres)(# Choices for VP)(# Sec)(#Tres) 20 15 316, 800 different choices 33 32

Permutation: A permutation of n distinct elements taken r at a time is an

Permutation: A permutation of n distinct elements taken r at a time is an ordered arrangement, without repetitions, of r of the n elements. The number of permutations of n elements taken r at a time is denoted by Example: How many three letter combinations can be made from 26 letters if No duplication is allowed? X 1 st 26 choices X 2 nd 25 choices X 3 rd 24 choices

Factorial Notation: Example: In how many ways can four coins be arranged in a

Factorial Notation: Example: In how many ways can four coins be arranged in a row? (quarter, nickel, dime, penny)

Example: A family of 5 consisting of the parents and 3 children are going

Example: A family of 5 consisting of the parents and 3 children are going to be arranged in a row by a photographer. If the parents are to be next to each other, how many arrangements are possible? How many other possible ways?

Evaluate:

Evaluate:

Using ABCDE, how many 3 letter words can be formed if repetitions are NOT

Using ABCDE, how many 3 letter words can be formed if repetitions are NOT allowed? Using ABCDE, how many 3 letter words can be formed if repetitions are allowed?

Group Problem If you have 5 signal flags and can send messages by hoisting

Group Problem If you have 5 signal flags and can send messages by hoisting one or more flags on a pole. How many messages can you send? (order matters)

THE FUNDAMENTAL COUNTING PRINCIPLE PERMUTATIONS THE FUNDAMENTAL COUNTINGTHE FUNDAMENTAL COUNTING PRINCIPLE PERMUTATIONS THE FUNDAMENTAL COUNTING
Fundamental Counting Principle Permutations Objectives apply fundamental countingFundamental Counting Principle Permutations Objectives apply fundamental counting
PERMUTATIONS PERMUTATIONS OF SIMILAR THINGS PERMUTATIONS PERMUTATIONS OFPERMUTATIONS PERMUTATIONS OF SIMILAR THINGS PERMUTATIONS PERMUTATIONS OF
Counting Principle The Fundamental Counting Principle The CountingCounting Principle The Fundamental Counting Principle The Counting
The Fundamental Counting Principle The fundamental counting principleThe Fundamental Counting Principle The fundamental counting principle
The Fundamental Counting Principal Permutations The Fundamental CountingThe Fundamental Counting Principal Permutations The Fundamental Counting
Counting Principles Mulitplication Counting Principle Addition Counting PrincipleCounting Principles Mulitplication Counting Principle Addition Counting Principle