1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
1. How many 2-side-dish meals can be made from 6 choices of side dishes?
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?
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? 15 12 36

3. 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.) ?? ?? = 27 54 19 38
Possible answer: =

4. Learn to find the number of possible permutations.

5. Vocabulary
permutation
factorial

6. 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.

7. 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.
T, B, A
B, T, A
A, T, B
T, A, B
B, A, T
A, B, T
There are 6 ways to order the letters.

8. 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
red, blue, orange
orange, red, blue
orange, blue, red
blue, orange, red
blue, red, orange
List all permutations beginning with red, then orange, and then blue.
There are 6 ways to order the colors.

9. You can use the Fundamental Counting Principle to find the number of permutations.

10. 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.

11. The Fundamental Counting Principle states that you can find the total number of outcomes by multiplying the number of outcomes for each separate experiment.
Remember!

12. 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.

13. zero that are less than or equal to the number.
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.

14. 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.

15. 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.

16. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 16 16 16 16

17. Lesson Quiz
1. In how many different ways can Anna, Barbara, and Cara sit in a row?
3. In how many different ways could 4 people enter a roller-coaster car?
4. 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? 6 24
720

18. 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 18 18 18 18

19. 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 19 19 19 19

20. 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 20 20 20 20