Permutations and Combinations

Slides:

Advertisements

Similar presentations

Essential Question: What are the two types of probability?

Advertisements

Permutations vs. Combinations

Section 3-6 Counting. FUNDAMENTAL COUNTING RULE For a sequence of two events in which the first event can occur m ways and the second event can occur.

Chap 2 Combinatorial Methods Ghahramani 3rd edition.

1 Many people debate basic questions of chance in games such as lotteries. The Monty Hall problem is a fun brain teaser that Marilyn vos Savant addressed.

Probability And Expected Value ————————————

Counting If you go to Baskin-Robbins (31 flavors) and make a triple-scoop ice-cream cone, How many different arrangements can you create (if you allow.

Chapter 7 - Part Two Counting Techniques Wednesday, March 18, 2009.

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

Statistics Probabilities

5.5 Counting Techniques. More Challenging Stuff  The classical method, when all outcomes are equally likely, involves counting the number of ways something.

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.

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

Evaluating a Permutation

6.2 Find Probability Using Permutations. Vocabulary n factorial: product of integers from 1 to n, written as n! 0! = 1 Permutation: arrangement of objects.

Section Copyright © 2014, 2012, 2010 Pearson Education, Inc. Lecture Slides Elementary Statistics Twelfth Edition and the Triola Statistics Series.

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.

Section 7.1. Section Summary Finite Probability Probabilities of Complements and Unions of Events Probabilistic Reasoning.

March 10, 2015Applied Discrete Mathematics Week 6: Counting 1 Permutations and Combinations How many different sets of 3 people can we pick from a group.

3.5 Probabilities Using Combinations. Scratch Tickets What is your probability of winning grand prize? Numbers are are picked Order of picking.

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.

Chapter 10 – Data Analysis and Probability

Basic Probability Permutations and Combinations: -Combinations: -The number of different packages of data taken r at time from a data set containing n.

Probability Permutations and Combinations.  Permutations are known as any arrangement of distinct objects in a particular _________. Permutations order.

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

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

Lesson # 65 Notes Combinations. Lesson # 65 Combinations.

Whiteboardmaths.com © 2004 All rights reserved

Honors Precalculus: Do Now 1.) A game consists of rolling a die. You receive the face value in dollars if an odd number is rolled. If the game costs $1.50.

Arrangements How many ways can I arrange the following candles?

ICS 253: Discrete Structures I Discrete Probability King Fahd University of Petroleum & Minerals Information & Computer Science Department.

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 calculus Problem of the Day H. W. - worksheet and p all Number of objects, n Size of group chosen from n objects

The Mean of a Discrete Random Variable Lesson

EXAMPLE 2 Use a permutations formula Your band has written 12 songs and plans to record 9 of them for a CD. In how many ways can you arrange the songs.

P(B) = Triangle Area P(A) = Oval Area P(A or B) = r + w + g P(A and B) = w So, P(A) + P(B) = r + w + g + w The Addition Rule for 2 events A and B P(A or.

Section 7.1. Probability of an Event We first define these key terms: An experiment is a procedure that yields one of a given set of possible outcomes.

Suppose a sequence begins 2, 4, …………………. Would could the formula be?

Probability and Counting Rules 4-4: Counting Rules.

Counting Techniques (Dr. Monticino). Overview  Why counting?  Counting techniques  Multiplication principle  Permutation  Combination  Examples.

Introduction to probability (2) Combinations التوافيق Definition of combination: It is a way of selecting items from a collection, such that the order.

Powerball Software - Does it Actually Work?. The Powerball Lottery is becoming quite popular in Florida nowadays. The game entails taking out 5 balls.

1 2.3 Counting Sample Points (6)(6)(6)= 216 Example: How many outcome sequences are possible when a die is rolled three times?

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.

EXAMPLE FORMULA DEFINITION 1.

The Pigeonhole Principle

Probability and Combinatorics

Probability Axioms and Formulas

Section 4.7 Counting – Day 1.

6.7 – Permutations and Combinations

Stat 100 Feb. 18.

Section 3-4 Permutations

Permutations and Combinations

Elementary Statistics

..J.ACKPOT. 13,

4 Probability Lesson 4.8 Combinations and Probability.

Permutations and Combinations

Chapter 7 Logic, Sets, and Counting

6-7 Permutations and Combinations

HWTP- practice for the test

Counting Methods and Probability Theory

12.2 Find Probability Using Permutations

Now it’s time to look at…

Counting Methods and Probability Theory

6.5 Find Expected Value MM1D2d.

Presentation transcript:

Permutations and Combinations Unit 6 Continued…

Definitions Permutations – order important Combinations – any order You need to know n! (“n factorial”) Ex: 4! = Ex: 7! =

Formulas Permutations Combinations r = items chosen n = total possible items

Example 1 Suppose you have four personalized letters and four addressed envelopes. If the letters are randomly placed in the envelopes, what is the probability that all four letters will go to the correct addresses? This is order important – permutation

Example 2 In a “pick 6” lottery, 54 numbered balls are used. Out of these, 6 are randomly chosen. To win, at least 3 balls must be matched in any order. What is the probability of winning the jackpot (all 6 balls)?

Same groups as yesterday! Work on assignment together! I will be marking off points for people who are not using their time wisely or talking about other things!