Transcript Permutations

10-8 Permutations
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
10-8 Permutations
Warm Up
1. How many 2-side-dish meals can be made from 6
choices of side dishes? 15
2. Kim has shorts in blue, black, and tan. She has
shirts in blue, yellow, red, and green. How many
different combinations can she make? 12
3. If you go to the movies and are allowed to get 2
snacks and there are 9 snacks to choose from, how
many combinations are there to pick from? 36
10-8 Permutations
Problem of the Day
Replace each ? with a different digit from
1 through 9 to make a proportion.
(Hint: The digits are not being multiplied.)
?? = ??
??
??
Possible answer: 27 = 19
54 38
10-8 Permutations
I can find the number of possible
permutations.
10-8 Permutations
Vocabulary
permutation
factorial
10-8 Permutations
An arrangement of objects or events in which
the order is important is called a permutation.
You can use a list to find the number of
permutations of a group of objects.
10-8 Permutations
Additional Example 1: Using a List to Find
Permutations
In how many ways can you arrange the
letters A, B, and T ?
Use a list to find the possible permutations.
A, B, T
B, A, T
T, A, B
A, T, B
B, T, A
T, B, A
There are 6 ways to order the letters.
10-8 Permutations
Check It Out: Example 1
In how many ways can you arrange the
colors red, orange, blue?
Use a list to find the possible permutations.
red, orange, blue List all permutations beginning
red, blue, orange with red, then orange, and then
orange, red, blue blue.
orange, blue, red
blue, orange, red
blue, red, orange
There are 6 ways to order the colors.
10-8 Permutations
You can use the Fundamental Counting
Principle to find the number of
permutations.
10-8 Permutations
Additional Example 2: Using the Fundamental
Counting Principle to Find the Number of
Permutations
Mary, Rob, Carla, and Eli are lining up for lunch. In how
many different ways can they line up for lunch?
Once you fill a position, you have one less choice for
the next position.
There are 4 choices for the first position.
There are 3 remaining choices for the second position.
There are 2 remaining choices for the third position.
There is one choice left for the fourth position.
4 · 3 · 2 · 1 = 24
Multiply.
There are 24 different ways the students can line up for lunch.
10-8 Permutations
Remember!
The Fundamental Counting Principle states
that you can find the total number of
outcomes by multiplying the number of
outcomes for each separate experiment.
10-8 Permutations
Check It Out: Example 2
How many different ways can you rearrange
the letters in the name Sam?
Once you fill a position, you have one less choice for
the next position.
There are 3 choices for the first position.
There are 2 remaining choices for the second position.
There is one choice left for the third position.
3 · 2 · 1= 6
Multiply.
There are 6 different ways the letters in the
name Sam can be arranged.
10-8 Permutations
A factorial of a whole number is the
product of all the whole numbers except
zero that are less than or equal to the
number.
“3 factorial” is 3! = 3 · 2 · 1 = 6
“6 factorial” is 6! = 6 · 5 · 4 · 3 · 2 · 1 = 720
You can use factorials to find the
number of permutations.
10-8 Permutations
Additional Example 3: Using Factorials to Find the
Number of Permutations
How many different orders are possible for
Shellie to line up 8 books on a shelf?
Number of permutations = 8!
=8·7·6·5·4·3·2·1
= 40,320
There are 40,320 different ways for Shellie to line
up 8 books on the shelf.
10-8 Permutations
Check It Out: Example 3
How many different orders are possible for
Sherman to line up 5 pictures on a desk?
Number of permutations = 5!
=5·4·3·2·1
= 120
There are 120 different ways for Sherman to line
up 5 pictures on a desk.
10-8 Permutations
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
10-8 Permutations
Lesson Quiz
1. In how many different ways can Anna,
Barbara, and Cara sit in a row? 6
2. In how many different ways could 4 people
enter a roller-coaster car? 24
3. How many different orders are possible for 6
basketball players to sit on the bench while
waiting to be announced at the beginning of a
game? 720
10-8 Permutations
Lesson Quiz for Student Response Systems
1. Identify the number of ways you can arrange
the letters in the word “MATH”.
A. 4
B. 6
C. 16
D. 24
10-8 Permutations
Lesson Quiz for Student Response Systems
2. In how many different ways can you arrange the
numbers 1, 3, 5, 7, 9 to make a 5-digit number
without any repetitions?
A. 5
B. 25
C. 120
D. 720
10-8 Permutations
Lesson Quiz for Student Response Systems
3. Janet has 9 antique pieces. In how many
different ways can she arrange them on a shelf?
A. 362,880
B. 40,320
C. 81
D. 9