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Allows us to represent, and quickly calculate, the number of different ways that a set of objects...
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Transcript of Allows us to represent, and quickly calculate, the number of different ways that a set of objects...
![Page 1: Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be arranged. Ex: How many different ways can a coach.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649ebb5503460f94bc3cad/html5/thumbnails/1.jpg)
![Page 2: Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be arranged. Ex: How many different ways can a coach.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649ebb5503460f94bc3cad/html5/thumbnails/2.jpg)
Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be
arranged.Ex: How many different ways can a coach organize the
three chosen shooters to take part in a shootout in a hockey game.
Player A
A
B
C
Player B
B
CA
CA
B
Player C
C
A
B
A
B
C
Resulting Order
ABC
ACBBAC
BCACAB
CBA
Using our tree diagram concept…
So there are 6 ways to order the shooters
![Page 3: Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be arranged. Ex: How many different ways can a coach.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649ebb5503460f94bc3cad/html5/thumbnails/3.jpg)
Ex: How many different ways can a coach organize the three chosen shooters to take part in a shootout in a
hockey game.
So there are 6 ways to order the shooters
An easier way to calculate the number of possible ways to order the shooter is to think about the choices at each
position.
Shooter 1 Shooter 2 Shooter 3
3 choices 2 choices 1 choice
3 1x2x = 6
![Page 4: Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be arranged. Ex: How many different ways can a coach.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649ebb5503460f94bc3cad/html5/thumbnails/4.jpg)
Factorial notation presents us with a method of easily representing the expression included on the last slide;
3 1x2x = 6
Written using factorial notation
3! Pronounced as “three factorial”Which means
![Page 5: Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be arranged. Ex: How many different ways can a coach.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649ebb5503460f94bc3cad/html5/thumbnails/5.jpg)
To multiply consecutive #’s we can use factorial notation.
Eg. 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 8!
Use your scientific calculator to solve!
40320 = 40320
Find: 3!= 5! = 10! =6 120 3,628,000
In general n! = n(n-1)(n-2)(n-3) . . . (3)(2)(1)
8 N!
![Page 6: Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be arranged. Ex: How many different ways can a coach.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649ebb5503460f94bc3cad/html5/thumbnails/6.jpg)
Working with the Notation
a) Simplify)!2(
!
nn
)!2(
)!2)(1(
n
nnn
)1( nn
c) Express 10 x 9 x 8 x 7 as a factorial.
!6
!10
b) Simplify!6
!8
56
!6
!678
![Page 7: Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be arranged. Ex: How many different ways can a coach.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649ebb5503460f94bc3cad/html5/thumbnails/7.jpg)
The group Major Lazer has 12 songs they want to sing at their show on Friday night. How many different set lists can be made?
12! 479001600
![Page 8: Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be arranged. Ex: How many different ways can a coach.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649ebb5503460f94bc3cad/html5/thumbnails/8.jpg)
10 students are to be placed in a row for photos. Katie and Jake must be beside each other. How many arrangements are there?
9! 2! 725760
K and J
![Page 9: Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be arranged. Ex: How many different ways can a coach.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649ebb5503460f94bc3cad/html5/thumbnails/9.jpg)
How many arrangements have them NOT beside each other?
10! (9! 2!)
6328800 72560
2903040
![Page 10: Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be arranged. Ex: How many different ways can a coach.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649ebb5503460f94bc3cad/html5/thumbnails/10.jpg)
![Page 11: Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be arranged. Ex: How many different ways can a coach.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649ebb5503460f94bc3cad/html5/thumbnails/11.jpg)
Pg 239 #1, 2, 7, 9, 11,12,13