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