6th Grade Math Textbook, Fundamentals

Lesson 12-7 for exercise sets. &KDSWHU 

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1.There are nine players on a baseball team. How many different

batting lineups are possible?

2.How many different ways can you arrange 5 DVDs on a shelf?

3.How many four-letter arrangements can you make from the letters in

the word NUMBER?

4.Rachel is in charge of selling yearbooks. She has nine student volunteers

to help her, and she needs to fill three positions: collecting money, unpacking

yearbooks from the boxes, and handing out yearbooks. In how many different

ways can the jobs be assigned to any three of the nine volunteers?

5.Discuss and Write Explain why 9! is notthe solution to problem 4 above.

Describe a problem that would have 9! as the solution.

How many different 3-digit security codes can be made if no digit repeats?

Digits: 0–9 10 digits in all 10 • 9 • 8  720

720 different 3-digit security codes can be made if no digit repeats.

1

Think

There are 10 choices for the first digit.

There are 9 choices for the second digit.

There are 8 choices for the third digit.

Think

You cannot use

factorials to solve

this problem.

Sometimes a permutation concerns only partof a list to be ordered.

Jill received five new books for her birthday. She decided to read two

books immediately and to save the other three books to read during the

summer. In how many different ways can Jill read two of the five books?

Here are two possible methods for solving the problem.

Method 1 Make a Tree Diagram

Let 1, 2, 3, 4, and 5 represent the five different books.

There are 20 different possibilities.

Method 2 Use the Fundamental Counting Principle

There are 5 choices when deciding which book to read first.

There are 4 choices that remain for the second book.

Number of book choices 5 • 4  20

So there are 20 different ways for Jill to read two of the five books she received.

2

3

4

5

1

1

3

4

5

2

1

2

4

5

3

1

2

3

5

4

1

2

3

4

5

1st

choice

2nd

choice

1st

choice

2nd

choice

1st

choice

2nd

choice

1st

choice

2nd

choice

1st

choice

2nd

choice