Permutations Examples 1. How many different starting rotations could you make with 6 volleyball players? (Positioning matters in a rotation.)

Slides:

Advertisements

Similar presentations

Algebra 1 Glencoe McGraw-Hill JoAnn Evans Math 8H 12-3 Permutations and Combinations.

Advertisements

1 Counting Techniques: Possibility Trees, Multiplication Rule, Permutations.

12.1 Permutations When a question says ‘how many arrangment’..... Think BOXES For each space we have a box In the box write down how many options can go.

Combinations, Permutations, and the Fundamental Counting Principle.

Counting Methods Topic 7: Strategies for Solving Permutations and Combinations.

How many possible outcomes can you make with the accessories?

12.1 & 12.2: The Fundamental Counting Principal, Permutations, & Combinations.

Permutations and Combinations AII Objectives:  apply fundamental counting principle  compute permutations  compute combinations  distinguish.

Permutations and Combinations. Random Things to Know.

3.4 Counting Principles Statistics Mrs. Spitz Fall 2008.

9.6 Counting Principles Permutations Combinations.

Factorial, Permutations, Combinations Week 6 TEST # 2 – Next week!

Permutations Counting Techniques, Part 1. Permutations Recall the notion of calculating the number of ways in which to arrange a given number of items.

T HE F UNDAMENTAL C OUNTING P RINCIPLE & P ERMUTATIONS.

Permutations Lesson 10 – 4. Vocabulary Permutation – an arrangement or listing of objects in which order is important. Example: the first three classes.

3.4B-Permutations Permutation: ORDERED arrangement of objects. # of different permutations (ORDERS) of n distinct objects is n! n! = n(n-1)(n-2)(n-3)…3·2·1.

MATH104 Ch. 11: Probability Theory. Permutation Examples 1. If there are 4 people in the math club (Anne, Bob, Cindy, Dave), and we wish to elect a president.

Permutations and Combinations

Permutations Chapter 12 Section 7. Your mom has an iTunes account. You know iTunes requires her to enter a 7- letter password. If her password is random,

1 Fundamental Counting Principle & Permutations. Outcome-the result of a single trial Sample Space- set of all possible outcomes in an experiment Event-

Sports Camp Morning Camp AerobicsRunningYogaSwimmingWeights Afternoon Camp HikingTennisVolleyballSoftball List all the possible choices available on your.

Warm Up Evaluate  4  3  2   6  5  4  3  2 

Permutations, Combinations, and Counting Theory AII.12 The student will compute and distinguish between permutations and combinations and use technology.

Warm Up 2/1/11 1.What is the probability of drawing three queens in a row without replacement? (Set up only) 2.How many 3 letter permutations can be made.

Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 1 M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY S TATISTICS Section 3-6 Counting.

Permutations and Combinations

Permutations and Combinations. Objectives:  apply fundamental counting principle  compute permutations  compute combinations  distinguish permutations.

Permutations Review: (Counting Principle) 1.) Carol has 4 skirts, 3 blouses and 3 pairs of shoes. How many different outfits are possible? 2.) A bike license.

Permutations and Combinations Review: Counting Principle 1.) Carol has 4 skirts, 3 shirts, and 3 pairs of shoes. How many different outfits are possible?

ProbabilityProbability Counting Outcomes and Theoretical Probability.

Modeling Monday Follow Up The actual count of trees! TeacherOld TreesNew Trees Loggins Fox Lindahl Averages:

Permutations, Combinations, and Counting Theory

Algebra 2/TrigonometryName: __________________________ 12.1, 12.2 Counting Principles NotesDate: ___________________________ Example 1: You are buying.

9.6 The Fundamental Counting Principal & Permutations.

11.1A Fundamental Counting Principal and Factorial Notation 11.1A Fundamental Counting Principal If a task is made up of multiple operations (activities.

Counting Principle 1.Suppose you have three shirts (red, black, and yellow) and two pair of pants (jeans and khakis). Make a tree diagram to find the number.

What is a permutation? A permutation is when you take a group of objects or symbols and rearrange them into different orders Examples: Four friends get.

Lesson 0.4 (Counting Techniques)

37. Permutations and Combinations. Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another.

 Life Expectancy is 180 th in the World.  Literacy Rate is 4 th in Africa.

Combinations & Permutations Permutation => Order is important Combination => Order doesn’t matter Examples: Your Locker “Combination” The lunch line (might.

Permutations and Combinations

MATH260 Ch. 5: Probability Theory part 4 Counting: Multiplication, Permutations, Combinations.

11-7 Permutations Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.

0.4 Counting Techniques. Fundamental Counting Principle TWO EVENTS:If one event can occur in m ways and another event can occur in n ways, then the number.

Permutations and Combinations. Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another.

EXAMPLE 1 Count permutations

Multiplication Rule Combinations Permutations

Lesson 13.2 Find Probabilities Using Permutations

12-5 Combinations.

12.1 The Fundamental Counting Principle & Permutations

Lesson 11.6 – 11.7 Permutations and Combinations

6.2 Find Probability Using Permutations

Section 0-4 Counting Techniques

Permutations and Combinations

Warm Up Permutations and Combinations Evaluate  4  3  2  1

Lesson 11-1 Permutations and Combinations

Australia & Oceania ABC

How many possible outcomes can you make with the accessories?

Pettit 9-5 Notes Indicator- D7

MATH 2311 Section 2.1.

Counting Principle.

Warm Up – 4/22 - Tuesday A deli has a lunch special which consists of a sandwich, Soup, dessert, and a drink. They offer the following choices: Sandwich:

Section 6.4 Counting and Combinations with Multiple Cases

Probability Warm Up page 12- write the question you have 10 mins to complete it. See coaching on page 85.

Probability Review Day 1

A step by step instruction guide

MATH 2311 Section 2.1.

Presentation transcript:

Permutations Examples 1. How many different starting rotations could you make with 6 volleyball players? (Positioning matters in a rotation.)

Permutations Examples 1. How many different starting rotations could you make with 6 volleyball players? (Positioning matters in a rotation.) = 6! = 720 There are 6 options for the 1 st position, then 5 options remaining for the 2 nd position, 4 for the 3 rd position, etc., until there is only 1 option left for the last position.

Permutations Examples 2. How many different starting lineups could you make with 11 soccer players, if each player could play any position?

Permutations Examples 2. How many different starting lineups could you make with 11 soccer players, if each player could play any position? 11! = 39,916,800 There are 11 options for the 1 st position, then 10 options remaining for the 2 nd position, 9 for the 3 rd position, etc., until there is only 1 option left for the last position.

Permutations Examples 3. How many different starting lineups could you make with 11 soccer players, if only 1 player can play goalie, 5 players can play any of 5 forward positions, and 5 players can play any of 5 defense/midfield positions?

Permutations Examples 3. How many different starting lineups could you make with 11 soccer players, if only 1 player can play goalie, 5 players can play any of 5 forward positions, and 5 players can play any of 5 defense/midfield positions? 15!5! = 14,400 Only 1 player can play goalie. For the forwards, there are 5 options for the 1 st position, 4 options for the 2 nd, etc. It works the same for the 5 defenders.

Permutations Examples 4. How many seating charts could a teacher make with 18 students in a class, and 18 available desks?

Permutations Examples 4. How many seating charts could a teacher make with 18 students in a class, and 18 available desks? 18! = There are 18 options for the 1 st seat, then 17 options remaining for the 2 nd seat, 16 for the 3 rd seat, etc., until there is only 1 option left for the last seat.

Permutations Examples 5. How many seating charts could a teacher make with 18 students in a class, and 22 available desks?

Permutations Examples 5. How many seating charts could a teacher make with 18 students in a class, and 22 available desks? …765 = 22! / (4!) = There are 22 seats to choose from for the 1 st student, then 21 seats remaining for the 2 nd student, 20 for the 3 rd student, etc., until there are 5 seats left to choose from for the last student.

Permutations Examples 6. How many codes are possible for a lock that has 4 digits, and each digit can be a number 0-9?

Permutations Examples 6. How many codes are possible for a lock that has 4 digits, and each digit can be a number 0-9? = 10 4 = 10,000 You can repeat numbers, so each digit has 10 possibilities (0-9).

Permutations Examples 7. How many codes are possible for a lock that has 4 digits, and each digit can be a number 0-9 or a letter A-F?

Permutations Examples 7. How many codes are possible for a lock that has 4 digits, and each digit can be a number 0-9 or a letter A-F? = 16 4 = 65,536 The numbers 0-9 and the letters A-F form the hexadecimal system, which is frequently used with computers. As the name suggests there are 16 possibilities for each digit.

Permutations Examples 8. In how many ways can you arrange 20 books on a bookshelf, if they are in a single row?

Permutations Examples 8. In how many ways can you arrange 20 books on a bookshelf, if they are in a single row? 20! = There are 20 books to choose from for the 1 st position, then 19 books remaining for the 2 nd position, 18 for the 3 rd position, etc., until there is only 1 book left for the last position.

Permutations Examples 9. In how many ways can you rank your favorite 3 movies from a list of 10?

Permutations Examples 9. In how many ways can you rank your favorite 3 movies from a list of 10? 1098 = 720 The key word here is rank, indicating that order matters. Ranking A-B-C as your first three choices is different from ranking C-B-A as your first three choices. Because order matters, you do not need any division.

Permutations Examples 10. In how many ways can you rank your favorite 5 books from a list of 20?

Permutations Examples 10. In how many ways can you rank your favorite 5 books from a list of 20? = 20! / (15!) = P(20, 5) = 20 nPr 5 =1,860,480