Do Now 1. Find the number of permutations with 7 books taken 4 at a time. 2. Find the number of permutations of the letters in each word: TennesseeGeorgiaAlabama.

Slides:

Advertisements

Similar presentations

Permutations and Combinations

Advertisements

Permutations vs. Combinations

Permutations and Combinations and The Basics of Probability Theory.

EXAMPLE 3 Find a probability using permutations For a town parade, you will ride on a float with your soccer team. There are 12 floats in the parade, and.

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.

Combinations Accelerated Math II November 17, 2014.

Combinations, Permutations, and the Fundamental Counting Principle.

How many possible outcomes can you make with the accessories?

Warm-Up Complete in notes.

Permutations & Combinations

Expected value a weighted average of all possible values where the weights are the probabilities of each outcome :

Permutations and Combinations

College Algebra Fifth Edition

10.3 Combinations Objectives: Solve problems involving combinations. Solve problems by distinguishing between permutations and combinations. Standards:

Statistics Probabilities

40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Probability Lesson: PR-4 Fundamental Counting Principle Fundamental Counting Principle Learning.

Evaluating a Permutation

Permutations and Combinations. Pg 1.2 : How many different ways can you line up 5 skittles, each a different color? Pg 1.3 : How many different ways can.

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.

Permutations Linear and Circular. Essential Question: How do I solve problems using permutations?

What are we doing today? Have calculator handy Notes: Basic Combinatorics Go over quiz Homework.

At the local deli you can add two toppings to your sandwich. Draw a tree diagram to show how many ways you can select two different toppings for your sandwich.

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

10.3 Combinations Objectives: Solve problems involving combinations. Solve problems by distinguishing between permutations and combinations. Standards:

10.3 Combinations **Quiz over Tomorrow**

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

Honors Precalculus Counting and Probability Section 12.2: Permutations and Combinations IBTWW: 10/23/2015.

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

6.3Find Probabilities Using Combinations

Lesson # 65 Notes Combinations. Lesson # 65 Combinations.

Find Probabilities Using Combinations

10.3 Combinations Objectives: Solve problems involving combinations. Solve problems by distinguishing between permutations and combinations. Standards:

Do Now 4/28/11 Take out HW from last night. Take out HW from last night.  Text p. 617, #10-30 evens Copy HW in your planner. Copy HW in your planner.

Arrangements How many ways can I arrange the following candles?

Warm Up Which of the following are combinations?

Permutations and Combinations Review: Counting Principle 1.) Carol has 4 skirts, 3 shirts, and 3 pairs of shoes. How many different outfits are possible?

12-6 Properties of Probability. Event A and Event B 1) P(A and then B) = P(A) P(B) 2) P(A or B) = P(A) + P(B) 3) P(A or B) = P(A) + P(B)- P(A ∩ B) **

3.2 Combinations.

HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Section 7.2 Counting Our.

Discrete Math Section 15.3 Solve problems using permutations and combinations Read page Combinations and permutations.

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.

Choosing items from a larger group, when the order does not matter. This is different than permutations in chapter 11.2 – items had to be in a certain.

Permutations and Combinations

Chance of winning Unit 6 Probability. Multiplication Property of Counting  If one event can occur in m ways and another event can occur in n ways, then.

Special Topics. Calculating Outcomes for Equally Likely Events If a random phenomenon has equally likely outcomes, then the probability of event A is:

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

Copyright © Cengage Learning. All rights reserved. Probability and Statistics.

The Fundamental Counting Principle and Permutations 18.0 Students use fundamental counting principles to compute combinations and permutations Students.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 4.5.

How many ways could…?.  There are 9 boys and 8 girls in the student council at Hermitage High School. How many ways could a single student be selected.

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

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.

Warm Up Which of the following are combinations?

Probability Counting techniques.

Permutations 10.5 Notes.

12-5 Combinations.

Discrete Math Section 15.3 Solve problems using permutations and combinations Read page Combinations and permutations.

6.2 Find Probability Using Permutations

Permutations and Combinations

Warm Up Which of the following are combinations?

Advanced Combinations and Permutations

How many possible outcomes can you make with the accessories?

Counting Principle.

Accelerated Precalculus

12.2 Find Probability Using Permutations

Probability Warm Up page 12- write the question you have 10 mins to complete it. See coaching on page 85.

WUE Seventeen applicants want to interview with SAS. In how many ways can the 8 time slots be assigned? How many different ways can the letters of the.

Permutations and Combinations

Presentation transcript:

Do Now 1. Find the number of permutations with 7 books taken 4 at a time. 2. Find the number of permutations of the letters in each word: TennesseeGeorgiaAlabama

Pg ; 9-50 all 9. 4, , , , ,243, , , ,160

Continued… , , , ,814, ,459, ,366, ,909, ,252, ,518, , , , , ,107,

Continued…again…

Combinations

Essential Question: How do I solve problems involving combinations?

Formula:

Things you need to know: In a permutation, ORDER matters. In a combination, order does NOT matter. The value of combinations will be less than most permutations. You will use the nCr function in the calculator.

Problem Types: Determine the values for “n” (total number of objects) and “r” (the rate the objects are taken). “n” is always larger. Multiply the combinations together using the nCr key if there is more than one type of object. Find the probability of an event by dividing the product of individual combinations by the total number of combinations. Your answer is a %.

Example 1 Find the # of ways to purchase 3 different kinds of juice from a selection of 10 different juices. (The order in which they are chosen doesn’t matter, making this a combination). 10 C 3 = 120

Example 2 The difference between a permutation and a combination: COMBO: How many ways are there to choose a committee of 3 people from a group of 5? 5 C 3 = 10 Permutation: How many ways are there to choose 3 separate office holders (chairman, secretary, and treasurer) from a group of 5? 5 P 3 = 60

Example 3 How many different ways are there to purchase 2 CD’s, 3 cassettes, and 1 videotape from 7 CD titles, 5 cassette titles, and 3 videotape titles? 7 C 2 5 C 3 3 C 1 = 630

Example 4 In a recent survey of 25 voters, 17 favor a new city regulation and 8 oppose it. Find the probability that in a random sample of 6 respondents from this survey, exactly 2 favor the proposal regulation, and 4 oppose it = 5.4%

Assignment: Pg. 647, #’s 4-39a.

Pg. 647, 4-39a / % ,792,840

Continued… , % % % % 34. Combo 35. Combo 36. Permutation 37. Permutation 38. Permutation 39. 2,598,960