Name Class Date Practice
Form G
Permutations and Combinations
1. A band sells t-shirts in 3 sizes and 2 different colors. How many different
t-shirts are there to choose from? 6
2. Each player on the baseball team can
order a baseball bat using the table to
the right. How many choices does each
player have? 12 choices
Finish
Length
Wood Type
Natural
32”
Ash
Black
33”
Maple
34”
3. In how many different orders can 5 runners finish a race? 120 orders
4. Evaluate 7!. 5040
25!
5. What is the value of 24! ? 25
6. How many possible combinations of 3 items from a group of 5 are possible?
10 combinations
7. Evaluate 6 P3 . 120
8. A basketball coach will choose 5 players from a group of 8 players to start the
next game. How many different groups of starting players are possible? 56
9. What is the value of nC r when n = 7and r = 4? 35
10. What is the probability of randomly choosing a penny and a nickel from a cup
of coins that contains a penny, a nickel, a dime, and a quarter? 26 OR equivalent
fraction, decimal, or percent.
11. Three playing cards are randomly chosen from a set numbered from 1 to 7.
What is the probability that the chosen cards are numbered 1, 2 and 3?
approximately 0.17
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Name Class Date Practice (continued)
Form G
Permutations and Combinations
12. Recreation When renting a bike from a local bike shop, you can choose from
the types, sizes, and colors in the table shown below?
Type
Size
Color
Mountain
Small
Green
Medium
Red
Large
Blue
Cruising
Road
How many different choices do you have? 27
13. Open-Ended Use an example to explain why you can use n! to find the
number of possible orders for n objects. Answers will vary. Sample: There are
4 people in a race. There are 4 possible first-place finishers. Once the first place
finisher is determined, there are 3 possible 2nd -place, etc. So the number of
orders is 4 3 2 1 = 4! = 24. For a race with n people, there are n! possible
orders of finishing.
# # #
14. Reasoning A hiker has 2 pairs of hiking shoes, 3 different shirts, and
2 different pairs of shorts to choose from. How does the number of
combinations of shoes, shirts, and shorts change as the hiker adds shirts to his
collection? Explain. Each time the hiker adds a shirt to his collection, 4 additional
# #
# #
combinations are possible. The initial number of combinations is 2 3 2 = 12.
When another shirt is added, the number of combinations becomes 2 4 2 = 16.
15. Business For each weekly meeting of a group of business leaders, members
take turns being the note-taker, the facilitator, and the speaker. In how many
different ways can these positions be chosen from the 9 members? 504 ways
16. Writing Explain how the Fundamental Counting Principle is related to a tree
diagram. A tree diagram lists options of each type in columns, and links each type of
option to show outcomes. The Fundamental Counting Principle uses numbers only.
The numbers of options in each column of a tree diagram are multiplied, yielding the
number of possible outcomes.
17. A game at the fair involves ping-pong balls numbered 1 to 18. You can win a
prize if you correctly choose the 5 numbers that are randomly drawn. What
are your chances of winning? approximately 0.014
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Name Class Date Practice
Form K
Permutations and Combinations
1. A museum gift shop sells hats in 3 sizes and 3 different colors. How many
different hats are there to choose from? 9
2. A local store has options for buying televisions, shown in the table below.
Color
Screen size
Silver
32”
Black
36”
40”
How many different televisions are there to choose from? 6
3. In how many different orders can 6 students line up? 720 orders
4. Evaluate 4!. 24
5. Evaluate 6 P3 . 120
6. What is the value of nC r when n = 8 and r = 7? 8
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name Class Date Practice (continued)
Form K
Permutations and Combinations
7. Vacation When renting a car, you can choose from the types and colors in the
table shown below?
Type
SUV
Color
Green
Convertible
Red
Sedan
Blue
How many different choices do you have? 9
8. Five index cards numbered 2 to 6 are face down on a table. What is the
probability of randomly flipping over the cards numbered 2 and 3?
2 OR equivalent fraction, decimal, or percent.
10
9. Reasoning A skier has 2 pairs of skis, 2 pairs of boots, and 2 different pairs
of gloves to choose from for a day of skiing. If she buys another pair of gloves,
how many more combinations will be possible? 4
10. Sports From a team of 7 golf players, a coach will pick a captain, a manager,
and a scorekeeper. In how many different ways can the manager choose these
positions from the 7 players? 210 ways
11. Writing Explain why you can use 4! to find the number of orders in which
4 people can finish a race. There are 4 possible first-place finishers. Once the
first place finisher is determined, there are 3 possible 2nd -place, etc. So the
number of orders is 4 × 3 × 2 × 1 = 4! = 24.
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