6.2 Find Probability Using Permutations

Slides:



Advertisements
Similar presentations
EXAMPLE 2 Use the combinations formula You order a sandwich at a restaurant. You can choose 2 side dishes from a list of 8. How many combinations of side.
Advertisements

MATHCOUNTS TOOLBOX Facts, Formulas and Tricks
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.
How many possible outcomes can you make with the accessories?
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.
Permutations and Combinations With Beanie Babies.
6-7 Permutations & Combinations M11.E.3.2.1: Determine the number of permutations and/or combinations or apply the fundamental counting principle.
6.7 – Permutations and Combinations
EXAMPLE 5 Find permutations of n objects taken r at a time Music You are burning a demo CD for your band. Your band has 12 songs stored on your computer.
Permutations and Combinations. Random Things to Know.
Transparency 4 Click the mouse button or press the Space Bar to display the answers.
40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Probability Lesson: PR-4 Fundamental Counting Principle Fundamental Counting Principle Learning.
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.
Transparency 3 Click the mouse button or press the Space Bar to display the answers.
Permutations and Combinations Standards: MM1D1b. Calculate and use simple permutations and combinations.
Permutations.
Warm Up 1/31/11 1. If you were to throw a dart at the purple area, what would be the probability of hitting it? I I 5.
EXAMPLE 5 Find permutations of n objects taken r at a time Music You are burning a demo CD for your band. Your band has 12 songs stored on your computer.
Basic Probability Permutations and Combinations: -Combinations: -The number of different packages of data taken r at time from a data set containing n.
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.
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.
6.3Find Probabilities Using Combinations
Lesson # 65 Notes Combinations. Lesson # 65 Combinations.
Find Probabilities Using Combinations
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.
Permutations and Combinations. Objectives:  apply fundamental counting principle  compute permutations  compute combinations  distinguish permutations.
6.7 Permutations & Combinations. Factorial: 4! = 4*3*2*1 On calculator: math ==> PRB ==> 4 7! = 5040 Try 12!
How many ways can we arrange 3 objects A, B, and C: Using just two How many ways can we arrange 4 objects, A, B, C, & D: Using only two Using only three.
HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Section 7.2 Counting Our.
13.2 – Find Probabilities Using Permutations A permutation is an arrangement of objects in which order is important. For instance, the 6 possible permutations.
9-4 Permutations (pg ) Indicator – D7. Permutation: an arrangement, or listing, of objects in which order is important (you can use the to find.
© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 11 Counting Methods and Probability Theory.
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.
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.
Quiz: Draw the unit circle: Include: (1)All “nice” angles in degrees (2) All “nice” angles in radians (3) The (x, y) pairs for each point on the unit circle.
Algebra II 10.1: Apply the Counting Principle and Permutations.
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.
EXAMPLE 1 Count permutations
Chapter 10 Counting Methods.
Counting Methods and Probability Theory
Section 8.3 PROBABILITY.
Lesson 13.2 Find Probabilities Using Permutations
Permutations 10.5 Notes.
6.7 – Permutations and Combinations
Permutations and Combinations
Chapter 0.4 Counting Techniques.
Lesson 12.5 – 12.6 Permutations and Combinations
Quote of the Day The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. -Tobias.
Lesson 4.6! Part 1: Factorial Notation!
4 Probability Lesson 4.8 Combinations and Probability.
Permutations and Combinations
Permutations and Combinations
Wednesday by Dave And Brian
Counting, Permutations, & Combinations
Permutations and Combinations
Probability with Permutations and Combinations
How many possible outcomes can you make with the accessories?
MATH 2311 Section 2.1.
Counting Methods and Probability Theory
Counting Principle.
12.2 Find Probability Using Permutations
Permutations, Combinations & Counting Principle
Permutation – Order matters (a race)
Permutations and Combinations
An arrangement of objects in which order is not important.
MATH 2311 Section 2.1.
Presentation transcript:

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 where ORDER matters For n objects, it is written as nPn = n! If not all objects are taken at a time (only r taken), it is written as nPr =

How many ways can you arrange the letters in MATH? 1st choice 2nd choice 3rd choice 4th choice 4 3 2 1 Then, you multiply the options together. 4*3*2*1 is the same as saying 4!.

EXAMPLE 1 Count permutations Consider the number of permutations of the letters in the word JULY. a. In how many ways can you arrange all of the letters? SOLUTION a. Use the counting principle to find the number of permutations of the letters in the word JULY. = 24 There are 24 ways you can arrange all of the letters in the word JULY. ANSWER

EXAMPLE 1 Count permutations b. In how many ways can you arrange 2 of the letters? b. When arranging 2 letters of the word JULY, you have 4 choices for the first letter and 3 choices for the second letter. Number of permutations = Choices for 1st letter Choices for 2nd letter ANSWER There are 12 ways you can arrange 2 of the letters in the word JULY. = 4 3 = 12 This is the same as 4P2. 4 choices but only 2 taken.

GUIDED PRACTICE for Example 1 1. In how many ways can you arrange the letters in the word MOUSE? There are 120 ways you can arrange all the letters in the word MOUSE. ANSWER

GUIDED PRACTICE for Example 1 2. In how many ways can you arrange 3 of the letters in the word ORANGE? ANSWER There are 120 ways you can arrange 3 of the letters in the word ORANGE.

Use a permutations formula EXAMPLE 2 Use a permutations formula CD Recording 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 on the CD? SOLUTION To find the number of permutations of 9 songs chosen from 12, find 12P9. 12P9 = 12 ! (12 – 9)! Permutations formula = 12! 3! Subtract.

Use a permutations formula EXAMPLE 2 Use a permutations formula 12 11 10 9 8 7 6 5 4 3! 3! = Expand factorials. Divide out common factor, 3!. = 79,833,600 Multiply. There are 79,833,600 ways to arrange 9 songs out of 12. ANSWER

GUIDED PRACTICE for Example 2 3. WHAT IF? In Example 2, suppose your band has written 15 songs. You will record 9 of them for a CD. In how many ways can you arrange the songs on the CD? There are 1,816,214,400 ways. ANSWER

EXAMPLE 3 Find a probability using permutations PARADE For a town parade, you will ride on a float with your soccer team. There are 12 floats in the parade, and their order is chosen at random. Find the probability that your float is first and the float with the school chorus is second. SOLUTION STEP 1 Write the number of possible outcomes as the number of permutations of the 12 floats in the parade. This is 12P12 = 12!.

) ( EXAMPLE 3 Find a probability using permutations STEP 2 Write the number of favorable outcomes as the number of permutations of the other floats, given that the soccer team is first and the chorus is second. This is 10P10 = 10!. STEP 3 Calculate the probability. soccer team is first chorus is second P ( ) = 10! 12! Form a ratio of favorable to possible outcomes. = 10! 12 11 10! Expand factorials. Divide out common factor, 10!. 1 = 132 Simplify.