allows us to represent, and quickly calculate, the number of different ways that a set of objects...

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

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

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

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!

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

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

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

How many arrangements have them NOT beside each other?

10! (9! 2!)

6328800 72560

2903040

Pg 239 #1, 2, 7, 9, 11,12,13