Lesson 12.5, For use with pages 675-679

1. Choose one of 6 piano players and one of 3 singers.

Use the counting principle to find the number of possible choices.

2. Choose one of 4 movies and one of 5 snacks.

Lesson 12.5, For use with pages 675-679

1. Choose one of 6 piano players and one of 3 singers.

Use the counting principle to find the number of possible choices.

ANSWER 18

2. Choose one of 4 movies and one of 5 snacks.

ANSWER 20

Essential Questions

• What are the differences between permutations and combinations?

• What are the differences between odds and probability?

• How is probability used to make predictions?

• What are the differences between experimental and theoretical probabilities?

• Day Two of Section 12.5 Permutations

Define :– Permutation– Factorial

– Explain what the notation 7P3 means

Permutations

n = total to select from

r = the number you are selecting

GUIDED PRACTICE for Examples 1 and 2

4. Chris wants to see four movies that were released in the past month. In how many different orders can Chris watch the movies?

Choices for 1st place

Choices for 2nd

place

Choices for 3rd place

Choices for 4th place

4 3 2 1 Counting principle

Chris can watch the movies in 24 different orders.Or 4P4 = 24.

ANSWER

= 24

GUIDED PRACTICE for Examples 1 and 2

5. In how many ways can 7 runners finish in first, second, and third place?

Choices for first

Choices for second

Choices for third

7 6 5 Counting principle

ANSWER

There are 210 ways to finish the first, second, and third place.Or 7P3 = 210.

= 210

EXAMPLE 2 Counting Permutations

Band Competition

Twelve marching bands are entered in a competition. You can use the counting principle to count how many ways first, second, and third places can be awarded.

Choices for 1st place

Choices for 2nd

place

Choices for 3rd place

12 11 10 Counting principle

ANSWER

There are 1320 ways to award the three places.Or 12P3 = 1320.

= 1320

• Try these

• 6! =

• 7! =

• (7-3)! =

8! 3!

9!

6!

720

5040

24

6720

504

=

=

• A school-wide poll is asking students to rank 6 different musical bands from most favored to least favored.

• How many ways could the bands be arranged in order?– 6! = 720 ways Or 6P6 = 720

• How many ways are there to rank the 2 most favored out of these 6? – 6 x 5 = 30 ways or 6P2 = 30 ways

Page 678

10P4 = 5040

15P5 = 360,360

Page 678

Yes. 11! = 11 x ( 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

6P4 = 360

On Line Calculators

• Permutations and Combinations– http://www.calctool.org/CALC/math/

probability/combinations– http://www.mathsisfun.com/combinatorics/

combinations-permutations-calculator.html

• Factorials– http://joemath.com/math124/Calculator/

factorial.htm

• Assignment: Worksheet 12.5

• www.lewiscentral.k12.ia.us/shipp