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.

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.
Probability Jeopardy Final Jeopardy Simple Probabilities Permutations or Combinations Counting Principle Fractions Decimals Spinners Potpourri Q $100.
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.
When dealing with the occurrence of more than one event, it is important to be able to quickly determine how many possible outcomes exist.
Warm-Up Complete in notes.
Probability Slides subject to change
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.
4.1. Fundamental Counting Principal Find the number of choices for each option and multiply those numbers together. Lets walk into TGIF and they are offering.
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.
College Algebra Sixth Edition James Stewart Lothar Redlin Saleem Watson.
Let’s say you had 2 flavors of ice cream (Chocolate, Strawberry), 2 cones (Waffle, Sugar), and 4 toppings (Nuts, M&M’s, Oreo, Butterfinger). Create a tree.
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.
10-8 Counting Principles Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.
Section 3: Trees and Counting Techniques Example Suppose a fast food restaurant sells ice cream cones in two sizes (regular and large) and three flavors.
Vocabulary Tree Diagram – A way for counting possible outcomes Sample Space – List of all possible outcomes Event – Any collection of one or more outcomes.
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.
What are we doing today? Have calculator handy Notes: Basic Combinatorics Go over quiz Homework.
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
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.
Chapter 12 PROBABILITY Counting, Combinations, Permutations, Probability, Binomial Theorem.
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.
Arrangements How many ways can I arrange the following candles?
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.
ProbabilityProbability Counting Outcomes and Theoretical Probability.
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.
Monday, March 31, 2014 AIM: What is the Multiplication Counting Principle?  DO NOW: Kimberly has three pair of pants: one black, one red, and one tan.
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.
Warm Up For a main dish, you can choose steak or chicken; your side dish can be rice or potatoes; and your drink can be tea or water. Make a tree diagram.
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.
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.
Copyright © Cengage Learning. All rights reserved. Probability and Statistics.
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 Methods and Probability Theory
The Fundamental Counting Principle
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 Problem of the Day Lesson Presentation Lesson Quizzes.
The Counting Principle & Finding Sets
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.
Presentation transcript:

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 local Quickymart. You have three choices for entertainment: bowling, a movie or watching wrestling on TV. You have two choices for dessert: s'mores and pie. How many possible dates are there? When in doubt, make a chart!

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

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

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

Example 2 A mechanic offers three types 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 flavors. How many different single-cone ice-cream cones is it possible to buy at this store?

Example 4: A little more challenging! 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: Stepping it up! 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