6th Grade Math Textbook, Fundamentals

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A travel company offers 1-day vacation packages to Seattle. Customers
can choose from 6 museums, 3 restaurants, 2 parks, and 4 shopping
districts. How many different vacation packages are possible if customers
choose one attraction from each category?

Total possible vacation packages:

So the travel company offers 144 different 1-day vacation packages.

Lesson 12-2 for exercise sets.

Key Concept

Factorial

The expression n! is the product of all

positive integers that are less than or

equal to n.

Note that 1! 1 and 0! 1.

You can also use the Fundamental Counting Principle to find the number of

different ways a group of items can be ordered.

How many different ways can you arrange four DVDs on a shelf?

Let A, B, C, and D represent the four DVDs. Note that the choice you

make for each position affects the choices that are available for the next

position. For example, if you choose A as the first DVD, only B, C, and D

are available for the second DVD, and so on.

With this in mind, you can multiply to find the total number

of possible arrangements.

1 st 2 nd 3 rd 4 th

Position Position Position Position

4 choices • 3 choices • 2 choices • 1 choice  24 arrangements

You can arrange four DVDs on a shelf 24 different ways.

The product 4 • 3 • 2 • 1 can be represented in shorthand

as 4!, which is read as “4 factorial.” A of a given

integer is the product of all positive integers less than or

equal to that integer.

So 6! is equal to 6 • 5 • 4 • 3 • 2 • 1, or 720.

factorial

museum restaurant park shopping

choices choices choices choices

6 • 3 • 2 • 4  144

Find the value of each expression. Be sure to use the order of operations.

1.9! 2.5! • 0! 3.4! • 3! 4.6! 5! 5.

6.In how many ways can a group of 10 friends stand in a row for a picture?

7.A bank gives out 10-digit account numbers using only the numbers 0–9.

If numbers can repeat in a given account number, how many different

account numbers could the bank issue?

8.Discuss and Write Compare the advantages and disadvantages of using

the Fundamental Counting Principle versus using a tree diagram.

Give examples to support your answer.

12!

10!