9 4 permutations
TRANSCRIPT
![Page 1: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/1.jpg)
9-4 Permutations p 381
Find the number of permutations of a set of objects
![Page 2: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/2.jpg)
Work the hands on mini lab on page 381 with a partner
![Page 3: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/3.jpg)
We want to choose president and vice president from 4 people.
• Demonstrate with volunteers.
• Use the fundamental counting principle to find number of outcomes.
![Page 4: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/4.jpg)
A permutation is an arrangement, or listing, of objects in which order
is important.
• President and vice president vs committee members
![Page 5: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/5.jpg)
Example from mini lab
![Page 6: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/6.jpg)
Factorial (n!)
• 5!=5*4*3*2*1=120
![Page 7: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/7.jpg)
Find each of the following
1. 7!
2. 3!
3. 2!(3!)
![Page 8: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/8.jpg)
Ex) in how many ways can the starting six players of a volleyball team stand in a row for a picture?
• Turn and talk---why is this a permutation?
![Page 9: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/9.jpg)
Ex) The finals of the Middle School Appalachian League features 8
swimmers. In how many ways can the swimmers finish in first of second
place?
• Why is this permutation?
![Page 10: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/10.jpg)
Ex) A team of bowlers has five members who bowl one at a time. In how many orders can they bowl?
• Why is this permutation?
![Page 11: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/11.jpg)
A school fair holds a raffle with 1st, 2nd, and 3rd prizes. Seven people enter the raffle. How many ways can the three prizes be awarded?
![Page 12: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/12.jpg)
In how many ways can you arrange four books on a shelf.
![Page 13: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/13.jpg)
In how many ways can you award 1st and 2nd prize form a group of 6?
![Page 14: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/14.jpg)
In how many ways can 7 people line up at a ticket window?
![Page 15: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/15.jpg)
In how many ways can you arrange the letters in the word eighty?
![Page 16: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/16.jpg)
In how many ways can you choose a leading man and an understudy
from 11 actors?
![Page 17: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/17.jpg)
Coach Malone has an 8-member volleyball team. He told his team that he would start six different
players every game. How many games would it take to do this?
• Why is this not permutation?
![Page 18: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/18.jpg)
The International Club is selling hot dogs at eh Spring Carnival. Customers can select three toppings from among
chili, onions, cheese, mustard, or relish.
• Is this permutation?
![Page 19: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/19.jpg)
What are some key words that help you know it is a permutation?
![Page 20: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/20.jpg)
What are some key words that show it is not a permutation?
![Page 21: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/21.jpg)
Handout—left side onlyLINE CODES
• With a partner
![Page 22: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/22.jpg)
Journal
• How do you find a permutation?
![Page 23: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/23.jpg)
nPrn objects chosen r at a time
• A school fair holds a raffle with 1st, 2nd, and 3rd prizes. Seven people enter the raffle. How many ways can the three prizes be awarded?
7P3
![Page 24: 9 4 Permutations](https://reader036.vdocuments.mx/reader036/viewer/2022081512/558d3fe8d8b42acc4f8b469a/html5/thumbnails/24.jpg)
p 382: 3-19, 21, 22, 23