The Fundamental Counting Principle

Slides:

Advertisements

Similar presentations

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.

Advertisements

In your closet you have three different dress shirts and six different ties. Tomorrow night you have a band concert and you must wear one dress shirt and.

College Algebra Fifth Edition James Stewart Lothar Redlin Saleem Watson.

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

MATHPOWER TM 12, WESTERN EDITION Chapter 7 Combinatorics.

15.2 Counting Methods: Permutations

Counting Principles The Fundamental Counting Principle: If one event can occur m ways and another can occur n ways, then the number of ways the events.

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

When dealing with the occurrence of more than one event, it is important to be able to quickly determine how many possible outcomes exist.

EXAMPLE 1 Use a tree diagram Snowboarding

The Fundamental Counting Principle

6-7 Permutations & Combinations M11.E.3.2.1: Determine the number of permutations and/or combinations or apply the fundamental counting principle.

Probability Jeopardy Final Jeopardy Simple Probabilities Permutations or Combinations Counting Principle Find the Probability Independent Dependent Q.

12.1 The Counting Principle. Vocabulary  Independent Events: choice of one thing DOES NOT affect the choice of another  Dependent Events: choice of.

Lesson 7-1. Warm-up You are at a restaurant with a special for $10. You have the option to get: a) an appetizer and an entree or b) an entree and a dessert.

Probability 53 Fundamental counting principle 52 Factorials 51 Permutations 50 WP: Permutations 49 Combinations 48 WP: Combinations 53 Fundamental counting.

11-1: Permutations & Combinations

The Counting Principle Advanced Math Topics. Vocabulary Independent Events: choice of one thing does NOT affect the choice of another Independent Events:

Counting Techniques 0.4.

Fundamental Counting Principle Probability. Tree Diagrams (remember how to draw these?) You have a photo that you want to mat and frame. You can choose.

Chapter 10 Section 1 Apply the Counting Principle and Permutations In this assignment, you will be able to Use the Fundamental Counting Principle.

Lesson # 64 – 65 Notes Permutations and Combinations 1.The Counting Principle – The number of outcomes for an event is the product of the number of outcomes.

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

Probability Jeopardy Final Jeopardy Simple Probabilities Permutations or Combinations Counting Principle Binomial Geometric Probability Potpourri Q $100.

Chapter 10 – Data Analysis and Probability

PART 6 Probability. The Basics Definition 1: An experiment is an occurrence with a result that is uncertain before the experiment takes place. Definition.

Warm Up 1.A restaurant offers a Sunday brunch. With your meal you have your choice of 3 salads, 4 sides, 3 entrees and 5 beverages and you can have either.

Warm Up 1)In your own words define probability. 2)If you toss a coin 10 times, how many times SHOULD if come up heads?

THE COUNTING PRINCIPLE (ch 8.7 in the textbook) Goal: to use the counting principle to count the number of ways an event can happen.

 Roll a die, flip a coin  Unique 3 letter arrangements of CAT  Unique 4 digit arrangements of 1, 2, 3, 4.

Chapter 2 Section 2.3 Introduction to Combinatorics.

The Fundamental Counting Principle 10-6 Learn to find the number of possible outcomes in an experiment.

Thinking Mathematically

Discrete Mathematics, 1st Edition Kevin Ferland Chapter 6 Basic Counting 1.

Permutations, Combinations, and Counting Theory

9.6 The Fundamental Counting Principal & Permutations.

Bellwork Maria has an unidentified disease. She has the option to choose from three states in which to be treated. In each state, there are two research.

The Counting Principle Uses multiplication to find the number of possible ways two or more events can occur.

DAY 6: FUNDAMENTAL COUNTING PRINCIPLE Classwork: pptx examples in class Discrete Pre- Test (not a grade in HAC) Unit 2 Project- Due day 13 Homework (day.

© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 11 Counting Methods and Probability Theory.

C OUNTING P RINCIPLE Warm UP: List down what make up of a deck of cards. Name what you know about a deck of cards.

12.1 Counting Key Q-How many outcomes can an event have? Fundamental Counting Principle More than one event to take into account. Multiply all events.

You’re planning a date: dinner, entertainment, and dessert. You have two choices for dinner: Happy Meals at McDonald's or microwave burritos from the.

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.

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.

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

Fundamental counting principle Fundamental Counting Principal = Fancy way of describing how one would determine the number of ways a sequence of events.

Bell work Diagnostic Evaluation Please pick up a Pre-Assessment off the table as you come in to class, take a seat, and get started.

Counting Techniques Section 5.5. Objectives Solve counting problems using the Multiplication Rule Solve counting problems using permutations Solve counting.

Discrete Math Section 15.2 Apply the multiplication, addition, and complement principles My wardrobe consists of two pairs of pants and four shirts. How.

THE COUNTING PRINCIPLE CHAPTER 12 LESSON 1. VOCABULARY Outcome- The result of a probability experiment or an event. Sample Space- The set of all possible.

Warm Up Which of the following are combinations?

Counting Methods and Probability Theory

Copyright © Cengage Learning. All rights reserved.

4 Probability Lesson 4.7 The Multiplication Counting

12.1 The Fundamental Counting Principle & Permutations

Warm Up In your own words define probability.

Plimsouls "A Million Miles Away“ The Rolling Stones-Ruby Tuesday

Homework Review.

Homework Review.

Permutations and Combinations

Warm Up Which of the following are combinations?

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

The Counting Principle & Finding Sets

Determining the Number of Possible Outcomes

Counting Methods and Probability Theory

Fundamental Counting Principal

Warm Up Melanie is choosing an outfit for a job interview. She has four dresses, three blouses, five pairs of pants and three pairs of shoes to choose.

Counting Methods and Probability Theory

Presentation transcript:

The Fundamental Counting Principle

You’re planning a date: dinner, entertainment, and dessert. 2 choices for dinner: Happy Meals at McDonald's or microwave burritos from the local Quickymart 3 choices for entertainment: bowling, a movie or watching wrestling on TV 2 choices for dessert: s'mores and pie How many possible dates are there?

Do you really want to make a chart every time? __________________ Event 1: Dinner __________________ Event 2: Entertainment __________________ Event 3: Dessert

Fundamental Counting Principle Keep doing this for all the events that occur # of ways the second event can occur # of ways the first event can occur # of ways the third event can occur

Multiply those bad boys. Example 1 A fast food restaurant sells hot dogs, hamburgers, chicken sandwiches, and barbecue sandwiches. For sides, they offer French fries, hushpuppies, or onion rings. How many possible meal combinations are there? Multiply those bad boys. __________________ Event 1: Choose an entrée. __________________ Event 2: Choose a side.

Example 2 A mechanic offers three types of oil changes: standard, synthetic, and high mileage; two types of wiper blades: low profile, and heavy use; and two types of mufflers: chrome and matte black. How many possible combinations are there?

Example 3 An ice cream store offers three types of cones and 31 ice cream flavors. How many different single-scoop ice-cream cones is it possible to buy at this store?

Example 4 In a certain state, automobile license plates display three letters followed by three digits. How many such plates are possible if letter repetition is allowed?

Example 5 In a certain state, automobile license plates display three letters followed by three digits. How many such plates are possible if repetition of the letters is not allowed?

Factorial Notation! Denoted by n! and is called “n factorial” Only works if the number of items is equal to the number of spots being filled 3! = 3 x 2 x 1 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Example 6 In how many different ways can a race with six runners be completed? Assume there is no tie.

Solution Six possible choices for first place Five possible choices for second place Four choices for third place and so on… So, by the Fundamental Counting Principle, the number of different ways the race can be completed is: 6 x 5 x 4 x 3 x 2 x 1 = 6! = 720