Permutations and Combinations

Slides:

Advertisements

Similar presentations

Probability Topic 5: Probabilities Using Counting Methods.

Advertisements

Warm-Up Problem Can you predict which offers more choices for license plates? Choice A: a plate with three different letters of the alphabet in any order.

CSRU1100 Counting. Counting What is Counting “how many?” Counting is the process of determining the answer to a question of “how many?” for any given.

Chapter 2 Section 2.4 Permutations and Combinations.

Counting principle and permutations

Permutations and Combinations

Permutations and Combinations SWBAT find all the permutations and combinations for a set.

4. Counting 4.1 The Basic of Counting Basic Counting Principles Example 1 suppose that either a member of the faculty or a student in the department is.

DAY 2 OF CHAPTER 13 NOW LET’S THINK ABOUT FAMILIES WITH 3 CHILDREN A) CREATE A SAMPLE SPACE OF EQUALLY LIKELY OUTCOMES B) WHAT’S THE PROBABILITY A 3-CHILD.

Probability Topic 5: Probabilities Using Counting Methods.

College Algebra Sixth Edition James Stewart Lothar Redlin Saleem Watson.

DAY 3 OF CHAPTER 13 COLLEGE DORM LOTTERY! 57 COLLEGE STUDENTS APPLY FOR 3 VERY DESIRABLE ROOMS IN THE BEST DORM ON CAMPUS. 20 OF THESE 57 STUDENTS WERE.

Permutations and Combinations. Pg 1.2 : How many different ways can you line up 5 skittles, each a different color? Pg 1.3 : How many different ways can.

P ERMUTATIONS AND C OMBINATIONS Homework: Permutation and Combinations WS.

How many different ways can you arrange the letters in “may”?

Formulas and Principles. Math I Unit 4 If one event can occur in m ways and another event can occur in n ways, then the number of ways that both events.

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

Introduction to Counting Discrete Structures. A Multiplication Principle.

Chapter 4 Lecture 4 Section: 4.7. Counting Fundamental Rule of Counting: If an event occurs m ways and if a different event occurs n ways, then the events.

Pre-Algebra HOMEWORK Page 469 #1-12 ANSWERS.

Permutations and Combinations

Counting and Probability It’s the luck of the roll.

What are we doing today? Have calculator handy Notes: Basic Combinatorics Go over quiz Homework.

Chapter  Determine how many different possibilities are possible:  1. There are 3 different ice cream flavors and 5 different toppings. You.

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

Section 15.3 – Day 2 Counting. When do I use what? Rearranging things that are all different: Counting Principles (multiplication), Combinations, Permutations.

Chapter 13 Counting. Gambler’s Lucky Bet You and your team are going to be playing the lottery. In each round you will have different lotteries to select.

Lesson Counting Techniques. Objectives Solve counting problems using the Multiplication Rule Solve counting problems using permutations Solve counting.

Objectives Solve counting problems using the Multiplication Rule Solve counting problems using permutations Solve counting problems using combinations.

Prob/Stats Definition A permutation is an ordered arrangement of objects. (For example, consider the permutations of the letters A, B, C and D.)

Honors Precalculus Counting and Probability Section 12.2: Permutations and Combinations IBTWW: 10/23/2015.

10/23/ Combinations. 10/23/ Combinations Remember that Permutations told us how many different ways we could choose r items from a group.

Do Now 1. Find the number of permutations with 7 books taken 4 at a time. 2. Find the number of permutations of the letters in each word: TennesseeGeorgiaAlabama.

Counting Methods Review General Guidelines. Fundamental Counting Principle Each category outcome is independent of any other category outcome OR Items.

Lesson  The numerator and denominator of a theoretical probability are numbers of possibilities.  Sometimes those possibilities follow regular.

Lesson # 65 Notes Combinations. Lesson # 65 Combinations.

Sullivan Algebra and Trigonometry: Section 14.2 Objectives of this Section Solve Counting Problems Using the Multiplication Principle Solve Counting Problems.

Aim #10-7: How do we use the permutation formula? A permutation is an ordered arrangement of items that occurs when: No item is used more than once. The.

Quiz Plot the point: (-4, 2, -3) in the Cartesian space. Find the midpoint between the 2 points: P(1, 5, -7) and Q(-5, 3, -3) 3. Find the distance.

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

Permutations, Combinations, and Counting Theory

6.7 Permutations & Combinations. Factorial: 4! = 4*3*2*1 On calculator: math ==> PRB ==> 4 7! = 5040 Try 12!

HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Section 7.2 Counting Our.

Choosing items from a larger group, when the order does not matter. This is different than permutations in chapter 11.2 – items had to be in a certain.

Multiplication Counting Principle How many ways can you make an outfit out of 2 shirts and 4 pants? If there are m choices for step 1 and n choices for.

CHAPTER 4: PROBABILITY CONCEPTS 4.8 Counting Rules.

Special Topics. Calculating Outcomes for Equally Likely Events If a random phenomenon has equally likely outcomes, then the probability of event A is:

PreQuiz 12A Make a systematic list of all possible outcomes: You spin a spinner and flip a coin.

Quiz: Draw the unit circle: Include: (1)All “nice” angles in degrees (2) All “nice” angles in radians (3) The (x, y) pairs for each point on the unit circle.

SECTION 5.4 COUNTING. Objectives 1. Count the number of ways a sequence of operations can be performed 2. Count the number of permutations 3. Count the.

Fri 4/29 Lesson 11 – 1 Learning Objective: To use permutations & combinations to count possibilities Hw: 11-1 Fundamental Counting WS.

Counting Principle part 2 I. Math symbols and formulas for Counting Principles. A) Basic Counting Principle = m x n where you have m things and n things.

Fundamental Counting Principal

Multiplication Rule Combinations Permutations

Multiplication Counting Principle

Permutations 10.5 Notes.

combinaTorial Analysis

Elementary Statistics

4 Probability Lesson 4.8 Combinations and Probability.

PROBABILITY RULES.

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

Counting, Permutations, & Combinations

Pearson Unit 6 Topic 15: Probability 15-3: Permutations and Combinations Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007.

Counting Methods and Probability Theory

Counting Methods and Probability Theory

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

Probability Review Day 1

Presentation transcript:

Permutations and Combinations

Pg 1.2 and WS #1: How many different ways can you line up 5 skittles, each a different color? Pg 1.3 and WS#2: How many different ways can you line up just 3 of the 5 skittles? Worksheet #3: With a CRT review quiz, how many different ways could you arrange 4 questions from 9 topics we have studied this year: Worksheet #4: explain it to a class member that is absent today.

How many different ways can you choose 5 of the 5 skittles where order doesn’t matter? Pg 1.4 and WS #1: How many different ways can choose 3 of the skittles and by the way, the order doesn’t matter – RPY is the same as PRY Pg 1.5 Answer 7C3; 10C7; what does 6C2 mean? WS#2: Use the formula for combinations – nCr ? Worksheet #3: explain it to a class member that is absent today. : Worksheet #4: solve the problem

Ways to Count Selections Factorials Permutations Combinations

Pg 2.1- Using the pattern of letters and numbers, how many different license plates are possible for this style of Utah plate? Selection: how many possibilities for each element all multiplied together. One selection is independent of the next selection. B1) Motorcycle plates have 5 figures but the first 2 are letters while the last 3 are digits. How many possible different plates are there for Motorcycles?

Pg 2. 2- The access code for an ATM is 4 digits Pg 2.2- The access code for an ATM is 4 digits. How many different access codes are possible? Selection: how many possibilities for each element all multiplied together. One selection is independent of the next selection. B2) Your bank requires an access code of 4 places where you can use a digit or 2 special symbols * or #. How many more possible codes does this allow versus just using digits?

Pg 2.3- The login code for an email site is 5 characters, alternating letter-digit-letter-digit-letter. How many possible login codes are there? Selection: how many possibilities for each element all multiplied together. One selection is independent of the next selection.

Pg 2.4- The login code for an email site is 5 characters and can be letters or digits in any order. How many possible login codes are there? B3) The login code for an email site is 5 characters and can be letters or digits in any order but you can only use a letter or digit once. How many possible login codes are there?

B4)- Practice on notes: 1. 4! = 2. 6! = 3. 5!/3! = 4. 10!/9! = 5. 0! =

Permutations: order or arrangement matters ABCD is not the same as BACD even though they have the exact same elements. You may not use an element more than once. Pg 2.6- In a race with 8 runners, how many different finishes are possible? Use factorials or n!

To Arrange any “r” number of items from a total group of “n” number of items nPr = n!/(n-r)!

Practice: 1- You just downloaded 5 new albums to your iPod, and are eager to listen to them. How many different orders can you play the albums in? Pages 3.1 B5) You take your iPod to the mountains and select a playlist of your 10 favorite albums to be played in random order. You’ll be there long enough to hear 5 of them. How many different orders of albums could you get to listen to?

Combinations: order doesn’t matter ABCD is the same as BACD which is the same as CABD etc… Page 3.3- The betting slips of NJ’s pick-6 Loto game offer a field of numbers from 1 to 49. Each bettor chooses any 6 of them. You win the grand prize if you six numbers match those randomly chosen. How many different selections are possible? The r! cancels out all the repeats of the same set in a different order nCr = n!/r!(n-r)! Pg 1.10

C)- Practice on notes: A county legislature consists of 13 elected reps., 5 dems and 8 reps. They’re setting up a 4 person committee to study a new proposal to build a new library. How many different committees could be formed if the group will consist of: 1- 4 Rep. 2- 4 Dem. 3- 2 Dem & 2 Rep. 4- 3 Rep & 1 Rep. 5- 2 or 3 Rep. the rest Dem

Practice: A video rental store is going out of business and is offering “DVD grab bags”. You can buy a bag of 6 DVD’s made from a randomly selected group of 15 recently popular movies. The group of 15 included 4 comedies, 8 dramas and 3 animated features. What is the probability that your grab bag contains Remember P(E)= want/total Pg 4.1 & D1- 2 comedies, 3 dramas and 1 animated flick? Pg 4.2 & D2- nothing but dramas Pg 4.3 & D3- 3 of the comedies and 3 dramas