Permutations
10.5 Notes
Entry Task

You have 100 songs on your iPhone. How many different
playlists can be created if you are choosing 5 songs?

(A song played first is different than if the song is played
second)

100*99*98*97*96
Example 1

You are going on vacation and you pack 3 sweaters, 4
pants, and 2 pairs of shoes. How many outfits are there?
Answer

3x4x2= 24 outfits
Example 2

Suppose a set of license plates has any three letters from
the alphabet, followed by any three digits.

How many different license plates are possible?


26x26x26x10x10x10 = 17,576,000 possible plates
How many license plates will have no repeats of numbers or
letters?

26x25x24x10x9x8=11,232,000 possible plates
Example 3





There are 5 starters on a basketball team; _______,
_______, _______, _______, and _______
The announcer doesn’t want to play favorites, so he will
announce their names in random order. How many
possible combinations are there?
5x4x3x2x1 = 120 possible combinations
OR
5! = 120
Factorial

n! = n(n-1)(n-2)(n-3)…1

Example:


3! = 3*2*1=6
Note:

0! = 1
Practice – No Calculator

3!

5!/3!
Example A – Part 1

Seven flute players are performing in an ensemble. How
many different ways can they be arranged?

What is the probability of the names of the flute players
being selected in alphabetical order?
(Remember: Probability is found by dividing the number
of ways an event can occur by the number of possible
outcomes)

Permutations


What is a permutation?
An arrangement of some or all objects of a set without
replacement where order matters.
n!
n Pr 
(n  r )!

n is the total # objects
r is # chosen
Find Permutations on your Calculator!
Example A – Part 1 (Using Permutations)

Seven flute players are performing in an ensemble. How
many different ways can they be arranged?

What is the probability of the names of the flute players
being selected in alphabetical order?
(Remember: Probability is found by dividing the number
of ways an event can occur by the number of possible
outcomes)

Example A – Part 2

After the performance, the players are backstage. There is
a bench with 4 seats. How many possible seating
arrangements are there?
Route 1: Counting Principle
Route 2: Use Permutations!
Example A – Part 2

After the performance, the players are backstage. There is
a bench with 4 seats. How many possible seating
arrangements are there?
Route 1: Counting Principle
Route 2: Use Permutations!
Example A – Part 3

What about if the bench has 5 seats?
Route 1: Counting Principle
Route 2: Use Permutations!
Example A – Part 3

What about if the bench has 5 seats?
Route 1: Counting Principle
Route 2: Use Permutations!
Permutation Practice (No Calc)
12!
9!
10
P2
n
P2
Assignment

Pg. 590 #1, 2aefg, 3ab, 4, 5, 8, 9abc, 11

Quiz 6/1
10.5-10.6 (permutations and combinations + Counting
Principle)

Example B

Two cards are drawn at random from a standard 52 card
deck. How many possible combinations are there?
Example B – Part 2

What is the probability of drawing a 7 and a king?