6th Grade Math Textbook, Progress

Update your skills. See page 16

8-15

6 teams

AB 
BA

12 teams

Permutations and Combinations

Two students from a team of 4 will go to the city math

contest. How many different teams can be formed?

To find how many teams, make an organized list.

Let A, B, C, and D represent each of the four students.

I. Order does not matter:

AB AC AD BC BD CD

Six teams can be formed.

If one is the contestant and the other is the alternate,

how many different teams can be formed?

II. Order matters: AB BA AC CA AD DA BC CB BD DB CD DC

When order matters, as in team II, you are counting permutations.

When order does not matter, as in team I, you are counting combinations.

You can also use the Counting Principle

to find permutations and combinations.

A. Three out of 5 students can win an essay contest.

How many different ways can the winners be selected?

To find the number of ways, find the number of

permutations since the order matters.

choices for choices for choices for total number

1st place 2nd place 3rd place of ways

5  4  3  60

There are 60 ways of selecting the winners.

B. Tony can only take 3 out of 5 subjects offered during the marking period.

How many different ways can he choose the subjects he will take?

To find the numbers of ways, find the number of combinations

since the order does not matter.

Find the number of arrange-

ments for each combination.

Divide to eliminate

duplicate combinations.

5  4  3  60 3  2  1  6 60  6  10

Tony has 10 ways of choosing the three subjects.

Find the number of

permutations of the items.

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