Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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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
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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

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I can find the number of possible permutations.
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Vocabulary
permutation factorial
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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.
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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.
There are 6 ways to order the letters.
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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.
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You can use the Fundamental Counting Principle to
find the number of permutations.
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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
Multiply.
24
There are 24 different ways the students can line
up for lunch.
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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
Multiply.
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There are 6 different ways the letters in the
name Sam can be arranged.
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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.
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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.
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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.
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Lesson Quiz

• 1. In how many different ways can Anna, Barbara,
  and Cara sit in a row?
• 2. In how many different ways could 4 people
  enter a roller-coaster car?
• 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?

6
24
720
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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
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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
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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