Counting Principles 1.What is 7! 7654321 = 5040 2.Which counting method do you use when order matters, a permutation or a combination? 3.Which is.

Slides:

Advertisements

Similar presentations

In this lesson we single out two important special cases of the Fundamental Counting Principle permutations and combinations. Goal: Identity when to use.

Advertisements

Permutations and Combinations

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.

U NIT : P ROBABILITY 6-7: P ERMUTATIONS AND C OMBINATIONS Essential Question: How is a combination different from a permutation?

Theoretical Probability

5.5 Permutations and Combinations When dealing with word problems, you must think: “Is there a specific order or is order disregarded?” This will tell.

Permutations and Combinations PRE-ALGEBRA LESSON Bianca’s family needs to choose exterior paint for their new house. The wall colors are white,

Probability Jeopardy Final Jeopardy Combinations Permutations Solve Comb or Perm Solve Q $100 $100Q $100 Q $200 Q $300 Q $400 Q $500.

Chapter 13 sec. 3.  Def.  Is an ordering of distinct objects in a straight line. If we select r different objects from a set of n objects and arrange.

MATHPOWER TM 12, WESTERN EDITION Chapter 7 Combinatorics.

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.

EXAMPLE 1 Counting Permutations Music You have five CDs. You can use the counting principle to count the number of permutations of 5 CDs. This is the number.

Multiplication Rule. A tree structure is a useful tool for keeping systematic track of all possibilities in situations in which events happen in order.

Permutations and Combinations. Random Things to Know.

Factorials How can we arrange 5 students in a line to go to lunch today? _________ __________ __________ __________ ________.

Aim: What is a permutation? Do Now: Evaluate n(n -1)(n-2)(n-3). 1. n = 52. n = 10.

8-2:Permutations and Combinations English Casbarro Unit 8.

Counting. Product Rule Example Sum Rule Pigeonhole principle If there are more pigeons than pigeonholes, then there must be at least one pigeonhole.

11-1: Permutations & Combinations

Math Duels Competition of Scholars. Rules  The class must be split into 2 groups.  Each group must select a team captain and they must do Rock-Paper-Scissors.

Bell work An Internet code consists of one digit followed by two letters. The number 0 and the letter “O” are excluded. How many different codes are possible?

Counting Principles. What you will learn: Solve simple counting problems Use the Fundamental Counting Principle to solve counting problems Use permutations.

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

1 Combinations. 2 Permutations-Recall from yesterday The number of possible arrangements (order matters) of a specific size from a group of objects is.

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.

Proportions Round One 2) x + 3 = 15 Answers 2.) x + 3 = 15 X=12 21.

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.

Pg. 606 Homework Pg. 631#1 – 3, 5 – 10, 13 – 19 odd #1135#12126 #1370#14220 #151365# #1756x 5 y 3 #1856x 3 y 5 #19240x 4 # x 6 #34expand to.

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

Permutations and Combinations Advanced Math Topics.

1 If a task is made up of multiple operations (activities or stages that are independent of each other) the total number of possibilities for the multi-step.

Permutations, Combinations, and Counting Theory

CLICK THE NUMBERS IN SEQUENCE

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

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

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.

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

7.3 Combinations Math A combination is a selection of a group of objects taken from a larger pool for which the kinds of objects selected is of.

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

Section 1.3 Each arrangement (ordering) of n distinguishable objects is called a permutation, and the number of permutations of n distinguishable objects.

Skip Counting Practice

Lesson 8-4 Combinations. Definition Combination- An arrangement or listing where order is not important. C(4,2) represents the number of combinations.

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

Knock Out!!!!! Your are in teams of four. The number on your desk corresponds to the number problem you are responsible for. When all four members of.

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.

Section 6-7 Permutations and Combinations. Permutation Permutation – is an arrangement of items in a particular order.

Example A standard deck of 52 cards has 13 kinds of cards, with four cards of each of kind, one in each of the four suits, hearts, diamonds, spades, and.

EXAMPLE 1 Count permutations

Multiplication Rule Combinations Permutations

Counting Methods and Probability Theory

6th – 9th Division Tournament

Chapter 0.4 Counting Techniques.

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

Section 0-4 Counting Techniques

Permutations and Combinations

Number Words two one three.

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

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

NUMBERS one two three four five six seven eight

Counting Methods and Probability Theory

Which is best value for money?

Permutations and Combinations

CLICK THE NUMBERS IN SEQUENCE

What is the difference between a permutation and combination?

Exercise How many different lunches can be made by choosing one of four sandwiches, one of three fruits, and one of two desserts? 24.

CLICK THE NUMBERS IN SEQUENCE

Presentation transcript:

Counting Principles 1.What is 7! 7*6*5*4*3*2*1 = Which counting method do you use when order matters, a permutation or a combination? 3.Which is a larger number, or ? 4. What is = 7*6*5 = What is=7*6*5/(3*2*1) = 210/6 =35

Counting Principles 6.Seven people are in a race. How many ways can they finish 1st, 2nd and 3rd? =7*6*5 = How many ways can you choose a team of three people from a group of seven? = 35 8.How many ways can you choose four people from a group of seven? = Why are you answers to seven and eight the same? Choosing 3 “winners” from seven is the same as choosing four “losers”

Counting Principles You have a Snickers bar, a bag of chips, a Reesy cup, a pack of Nabs and a Moon Pie in your bookbag. You plan to eat one item in each of your next two periods of school. How many ways can you do this? Consider each food different. = 20

Counting Principles There are 25 desks in Mr. Gillam’s class and he has 28 students. In how many different ways can they sit at a desk if all desks are filled and three student are left standing ? 5.8 x There are 25 desks in Mr. Gillam’s class and he has 28 students. How many different ways can you choose the three students who are left standing? 3276

Counting Principles You have to play 10 games of Grand Theft Auto IX: Blythewood to qualify for the tournament next month. You have 20 evenings left to play, and can play one game an evening. How many different schedules for playing the ten games are possible? You and six other people are in a tournament playing the Guitar Zero video game. How many ways can 1st, second and third place be awarded? 120

Counting Principles Bernie Madoff’s answering machine is full with 32 messages. If 32 distinct individuals called him with death threats, how many different orders could the calls have come in? 32! = 2.63 x 10 35

Counting Principles Seventy-five AIG employees are receiving bonuses. Five of these bonuses are greater than 4 million dollars. How many ways can you select the five employees to get the five large bonuses from the seventy-five employees If the government chooses three of the five employees in problem number 19 to testify at a congressional hearing, how many permutations of the order of the three testimonies are possible? 60

Counting Principles How many different arrangements are there of the letters in the word NERDY if repetition is not allowed? 5*4*3*2*1 = Which of the following is equivalent to n!? a) b) c) d) 42