15.2 Multiplication, Addition and Complement Principles

Slides:

Advertisements

Similar presentations

The Fundamental Counting Principle and Permutations

Advertisements

Counting Principles Probability.

Basic counting principles, day 1 To decide how many ways something can occur, you can draw a tree diagram. Note that this only shows half of the tree –

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

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.

___ ___ ___ ___ ___ ___ ___ ___ ___

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

Warm Up Use an inequality symbol to make each expression true a x 10 4 ___________ 5, 430 b. 32 ÷ ¼ ___________ 32 ÷4 c. 0.72___________¾.

A tree diagram is a segmented graph in the shape of a tree in which no branch leads from any vertex back to itself. Each path through it represents a mutually.

Probability Part 1 – Fundamental and Factorial Counting Rules.

Do Now: Make a tree diagram that shows the number of different objects that can be created. T-shirts: Sizes: S, M, L and T-shirts: Sizes: S, M, L and Type:

15.1 Factorial & Fundamental Counting Principles.

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,

Permutations With your group find as many arrangements of the letters A, H, M, T as you can. How many 2 letter arrangements are there? Could you do this.

Methods of Counting Outcomes BUSA 2100, Section 4.1.

Section 2.6: Probability and Expectation Practice HW (not to hand in) From Barr Text p. 130 # 1, 2, 4-12.

Unit 4 – Combinatorics and Probability Section 4.1 – Multiplication, Addition, and Complement Calculator Required.

Motivation Suppose you want tacos for lunch. The cafeteria has three tortilla choices: corn, flour and hard shell and four meat choices: ground beef,

Chapter 10 – Data Analysis and Probability

1 Lecture 4 (part 1) Combinatorics Reading: Epp Chp 6.

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

Larson/Farber Ch. 3 Weather forecast Psychology Games Sports 3 Elementary Statistics Larson Farber Business Medicine Probability.

March 10,  Counting  Fundamental Counting principle  Factorials  Permutations and combinations  Probability  Complementary events  Compound.

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

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

Algebra II 10.1: Apply the Counting Principle and Permutations HW: HW: p (6, 10, 14, 16, 26, 28, 34, all) Quiz : Friday, 12/13.

Find permutations using permutation notation and using technology.

Permutations – Page 1CSCI 1900 – Discrete Structures CSCI 1900 Discrete Structures Permutations Reading: Kolman, Section 3.1.

Fundamental Counting. How do you count? Try counting these dots… 5 7 5×7= 35 So, there are 35 dots. Is this any easier?

Happy 2014! Sit somewhere new to start the new year! The plan for this semester…

April 16, 2010Math 132: Foundations of Mathematics 8.6 Homework Solutions Annual % Rate: 7.0% Amount of Mortgage: $200,000 # of Monthly Payments: 240 Monthly.

Learning Objectives for Section 7.3 Basic Counting Principles

Counting The Fundamental Counting Principle. Fundamental Counting Principle If a series of “n” decisions must be made, and if the first decision can be.

Lesson #35 Outcomes and Probability. Probability is used in….

Fundamental Counting Theorm. Fundamental Counting Principle Fundamental Counting Principle can be used determine the number of possible outcomes when.

8-1: The Counting Principle English Casbarro Unit 8.

Each small square has sides of length 1 unit. How many distinct paths of length six units are there from A to B? A B..

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.

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.

Warm up How many possible pizzas could you make with 3 types of meats, 2 types of cheeses, and 2 types of sauces? 5 * 4 * 3 * 2 * 1 =

 Counting  Fundamental Counting principle  Factorials  Permutations and combinations  Probability  Complementary events  Compound events  Independent.

Probability Any event occurring as a result of a random experiment will usually be denoted by a capital letter from the early part of the alphabet. e.g.

Warm Up: 2/21/2012 Use completing the square. Fundamental Counting Principles  If one selection can be made in m ways, and for each of these a second.

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.

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.

INTRO TO COUNTING: 11.4 Day 1. SIMPLE ENUMERATION COLLECTION OF ITEMS THAT IS A COMPLETE, ORDERED LISTING OF ALL OF THE ITEMS IN THAT COLLECTION. How.

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.

Do Now A password must contain 4 characters. 1. How many passwords are possible if you just use digits in the password? 2. How many are possible with just.

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

Algebra II 10.1: Apply the Counting Principle and Permutations.

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

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.

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

Multiplication Counting Principle

12.2 Permutations and Combinations

1. In how many ways can six people sit in a six-passenger car?

Multiplying 2 Digit Factors

Permutations 10.5 Notes.

2 Digit by 2 Digit Multiplication

One, two, three, we’re… Counting.

Apply the Counting Principle and Permutations

Shift Patterns in multiplication

Counting, Permutations, & Combinations

Probability and Chance

6.2 Fundamental Counting Principal

Multiplication Principle for Counting

The Multiplication Principle

Warm Up Make your own burrito. Choice of Flour or Corn tortilla

Presentation transcript:

15.2 Multiplication, Addition and Complement Principles

The Multiplication Principle If an action can be performed in n1 ways, and for each of these ways another action can be performed in n2 ways, then the two actions can be performed in n1 n2 ways.

Actions being performed TOGETHER MULTIPLY

You have 2 shirts, 4 pairs of pants and 3 pairs of shoes, how many different shirt, pants and shoes outfits can be made?

The Addition Principle Two events that cannot be performed together are called MUTUALLY EXCLUSIVE. If two actions are mutually exclusive and the first can be done in n1 ways and the second in n2 ways, then one action OR the other can be done in n1+ n2 ways.

You have 2 blazers and 4 sweaters. A) How many blazer and sweater outfits can you wear? B) Suppose you decide to wear either a blazer or a sweater, but not both. How many choices do you have?

Actions NOT being performed together ADD

In how many ways can 7 people line up?

Factorials n! is defined as: n(n-1)(n-2)∙…∙3∙2∙1

How many different 9 person lineups can you create with a baseball team of 11 players?

How many license plates can be made using 3 letters followed by 3 digits?

How many different license plates can be made using 6 letters and digits in any order?

In Morse Code, the letters of the alphabet are represented by sequences of dots and dashes. Show that no more than 4 symbols (of dots and dashes) are needed to represent all of the alphabet.

The Complement Principle

Find the number of 4-digit numbers containing at least one digit 5 Find the number of 4-digit numbers containing at least one digit 5. (The first digit cannot be zero)

Given the digits 0,1,2,3,4,5 how many 4 digit numbers can be formed if (1st digit cannot be zero): a. Digits can be repeated? b. Digits cannot be repeated?

How many different ways can you make a license plate with 3 letters followed by 2 digits with at least 1 Q?

Homework P. 575 (Written Exercises) 1 - 8