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
Player B
Player C
Resulting Order
B
C
ABC
C
A
B
C
ACB
BAC
C
A
A
B
BCA
CAB
B
A
CBA
A
B
So there are
6 ways to
order the
shooters
C
Ex: How many different ways can a coach organize the
three chosen shooters to take part in a shootout in a
hockey game.
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
3 choices
3
Shooter 3
2 choices
x
2
1 choice
x
1 = 6
So there are 6 ways to order the shooters
Factorial notation presents us with a method of easily
representing the expression included on the last slide;
3
x
2
x
1 =
6
Written using factorial notation
Which means
3!
Pronounced as
“three factorial”
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!
8
N!
40320 = 40320
Find: 3!=
6
5! = 120
10! =
3,628,000
In general n! = n(n-1)(n-2)(n-3) . . . (3)(2)(1)
Working with the Notation
a) Simplify
n!
( n  2 )!

n ( n  1)( n  2 )!
( n  2 )!
 n ( n  1)
b) Simplify
8!

8  7  6!
6!
6!
 56
c) Express 10 x 9 x 8 x 7 as a factorial.

10 !
6!
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?
K and J
9 ! 2 !  7 2 5 7 6 0
How many arrangements have them
NOT beside each other?
10 ! (9 ! 2 !)
 6328800  72560
 2903040

Pg 239 #1, 2, 7, 9, 11,12,13