The previous lesson taught me how to use the Fundamental Counting Principle to count the number of possible outcomes of compound events. Today's lesson built on that by teaching me how to use permutations to calculate probabilities by taking the number of favorable outcomes and dividing by the total number of possible outcomes. Understanding how to count outcomes using the Fundamental Counting Principle was necessary to understand how to calculate probabilities using permutations, as the total number of possible outcomes is needed for the denominator of a probability fraction. So the previous lesson provided the foundation for understanding the key concepts and calculations in today's probability lesson.

1. Use the Fundamental Counting Principle to find the total number of
outcomes in each situation.
1. choosing north, south, east, or west and one of the 50 states
2. picking a day of the week and a month of the year
3. choosing vanilla, strawberry, chocolate, or mint chip ice cream with
fudge, butterscotch, strawberry, or whipped topping, in a cone or a cup
4. Margarita wants to wear a different outfit to school each day using her
new clothes. Margarita bought 5 pairs of pants, 9 shirts, and 4 pairs of
shoes. How many days of school does Margarita expect to have?
5. Ryan has a business screen printing T-shirts. Ryan offers 12 color
options, 3 T-shirt styles, and printing in 1, 2, 3, 4, or 5 colors. How many
different styles of T-shirts does Ryan’s business offer?
Course 2, Lesson 9-6

2. Course 2, Lesson 9-6
ANSWERS
1. 200
2. 84
3. 32
4. 180
5. 180

3. HOW can you predict
the outcome of future events?
Statistics and Probability
Course 2, Lesson 9-6

4. Course 2, Lesson 9-6 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Statistics and Probability
• 7.SP.8
Find probabilities of compound events using organized lists, tables,
tree diagrams, and simulation.
• 7.SP.8a
Understand that, just as with simple events, the probability of a
compound event is the fraction of outcomes in the sample space
for which the compound event occurs.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.

5. • To find a permutation
• To use permutations to find
probabilities
Course 2, Lesson 9-6
Statistics and Probability

6. Course 2, Lesson 9-6
Statistics and Probability
• permutation

7. 1
Need Another Example?
2
Step-by-Step Example
Julia is scheduling her first three classes. Her choices are math,
science, and language arts. Use the Fundamental Counting
Principle to find the number of different ways Julia can schedule
her first three classes.
1.
There are 3 choices for the first class.
There are 6 possible arrangements, or permutations,
of the 3 classes.
There are 2 choices that remain for the second class.
There is 1 choice that remains for the third class.
the number of permutations of 3 classes3 2• • 1 = 6

8. Answer
Need Another Example?
There are five people on a bowling team. If they bowl
one at a time, in how many orders can they bowl?
120

9. 1
Need Another Example?
2
3
Step-by-Step Example
An ice cream shop has 31 flavors. Carlos wants to buy a
three-scoop cone with three different flavors. How many
cones could he buy if the order of the flavors is important?
2.
There are 31 choices for the first scoop, 30 choices for
the second scoop, and 29 choices for the third scoop.
Use the Fundamental Counting Principle.
Carlos could buy 26,970 different cones.
31 • 30 • 29 = 26,970

10. Answer
Need Another Example?
Fifteen students are running for seventh grade student
council. In how many different ways can the president,
vice president, and secretary be chosen?
2,730

11. 1
Need Another Example?
Step-by-Step Example
Find P(8, 3).3.
P(8, 3) = 8 • 7 • 6 or 336 8 things taken 3 at a time

12. Answer
Need Another Example?
Find P(7, 2).
42

13. 1
Need Another Example?
2
3
4
Step-by-Step Example
Ashley’s MP3 player has a setting that allows the songs to play in a
random order. She has a playlist that contains 10 songs. What is the
probability that the MP3 player will randomly play the first three
songs in order?
4.
First find the permutation of ten things taken three at a
time or P(10, 3).
P(10, 3) = 10 • 9 • 8
= 720
So, there are 720 different ways to play the first 3 songs.
Since you want the first three songs in order, there is
only 1 out of the 720 ways to do this.
So, the probability that the first 3 songs will play in
order is .

14. Answer
Need Another Example?
Consider all of the five-digit numbers that can
be formed using the digits 1, 2, 3, 4, and 5,
where no digit is used twice. Find the probability
that one of these numbers picked at random ends
with a 5.
or 20%

15. 1
Need Another Example?
2
Step-by-Step Example
A swimming event features
8 swimmers. If each
swimmer has an equally
likely chance of finishing in
the top two, what is the
probability that Yumii will
be in first place and Paquita
in second place?
5.
First find the permutation of 8 things taken two at a time or P(8, 2).
P(8, 2) = 8 • 7
There are 56 possible arrangements, or permutations,
of the two places. Since there is only one way of having
Yumii come in first and Paquita second, the probability
of this event is .
= 56

16. Answer
Need Another Example?
A school fair holds a raffle with 1st, 2nd, and 3rd prizes.
Seven people enter the raffle, including Marc, Lilly, and
Heather. What is the probability that Marc will win the
1st prize, Lilly will win the 2nd prize, and Heather will
win the 3rd prize?

17. How did what you learned
today help you answer the
Course 2, Lesson 9-6
GeometryStatistics and Probability
HOW can you predict
the outcome of future events?

18. How did what you learned
today help you answer the
Course 2, Lesson 9-6
GeometryStatistics and Probability
HOW can you predict
the outcome of future events?
Sample answers:
• By using the Fundamental Counting Principle to find
the number of permutations
• By using permutations to find the probabilities of real-
world situations

19. The previous lesson was about
using the Fundamental Counting
Principle to find the number of
possible outcomes in a sample
space. How did the previous
lesson help you with today’s lesson?
Course 2, Lesson 9-6
Ratios and Proportional RelationshipsFunctionsStatistics and Probability