Combinations, Permutations, Counting
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by Nancy Compton
| 30 Questions
Note from the author:
This was modified from a GoFormative published by Sherri Stevenson to include combinations and the counting principle. Thank you, Sherri!
Some questions will ask for the type of problem prior to solving. Make sure you have these correct before continuing as they will help you to correctly set up the calculations for the answers.

Reminders:
  • The fundamental counting principle says that you can multiply the number of choices to determine the number of possibilities.
  • The "P", "C", and "!" operations are all located in the same place on most calculators.
  • Permutation means that the order (or arrangement) matters. Combination means you simply want a group.
1
1
9!
2
1

7P5

3
1

7C5

4
1

( 8P3 ) ( 4P2 )

5
1
Enter your answer as a fraction in lowest terms:

6C3 / 8C5

6
1
10!
8!2!

7
1
At the after school Hawk Club meeting, there were four drinks you could choose from: orange soda, Coke, Dr. Pepper, and water. There were three snacks you could choose from: peanuts, fruit, and cookies. Each student may have only one drink and one snack.
Use the fundamental counting principle to find the number of choices available
8
1
What kind of problem is this?
How many different choices are available for a car if there are 4 different body styles, three different types of engines, and 10 different colors?
combination
permutation
fundamental counting principle
9
1
Answer the question:
How many different choices are available for a car if there are 4 different body styles, three different types of engines, and 10 different colors?
10
1
How many different passwords can be made if it is three letters, followed by two digits, followed by a letter? (Repetition is allowed.) Use the fundamental counting principle.
11
1
What kind of problem is this?
The ski club has ten members to choose two co-captains. How many ways can these positions be filled?
combination
permutation
fundamental counting principle
12
1
Answer the question:
The ski club has ten members to choose two co-captains. How many ways can these positions be filled?
13
1
Which is the correct calculation and answer?
How many different ways can the word REFEREE be arranged?
7! = 5,040
7! / (4! 2!) = 105
7! / 4! 2! = 105
14
1
How many different ways can the word ELEMENTARY be arranged?
15
1
What kind of problem is this?
How many ways can 1st place, 2nd place, and 3rd place be chosen if there are 55 contestants in the beauty pageant?
combination
permutation
fundamental counting principle
16
1
Answer the question
How many ways can 1st place, 2nd place, and 3rd place be chosen if there are 55 contestants in the beauty pageant?
17
1
What kind of problem is this?
The batting order for eight players on a 10 person team.
combination
permutation
fundamental counting principle
18
1
Answer the question.
The batting order for eight players on a 10 person team.
19
1
What kind of problem is this?
The student body of 125 students wants to elect a president, vice president, and secretary. How many possible results are there?
combination
permutation
fundamental counting principle
20
1
Answer the question.
The student body of 125 students wants to elect a president, vice president, and secretary. How many possible results are there?
21
1
What kind of problem is this?
16 teams are in the Sweet 16 tournament. The top 2 will advance to the next level. How many ways can this happen?
combination
permutation
fundamental counting principle
22
1
Answer the question.
16 teams are in the Sweet 16 tournament. The top 2 will advance to the next level. How many ways can this happen?
23
1
What kind of problem is this?
You are determining the batting order for five players on a 12 person team and have narrowed the choices for the first position to 3 players and the second position to 4 players. How many 5-person line-ups are now possible?
combination
permutation
fundamental counting principle
24
1
Answer the question.
You are determining the batting order for five players on a 12 person team and have narrowed the choices for the first position to 3 players and the second position to 4 players. How many 5-person line-ups are now possible?
25
1
What kind of problem is this?
The five Smith children run to the ice cream truck. How many ways can they line up to order?
combination
permutation
fundamental counting principle
26
1
Answer the question.
The five Smith children run to the ice cream truck. How many ways can they line up to order?
27
1
What kind of problem is this?
In how many ways can the letters in "market" be arranged?
combination
permutation
fundamental counting principle
28
1
Answer the question.
In how many ways can the letters in "market" be arranged?
29
1
What kind of problem is this?
A volleyball squad has twelve players. How many ways can the players line up to greet the opposing team?
combination
permutation
fundamental counting principle
30
1
Answer the question.
A volleyball squad has twelve players. How many ways can the players line up to greet the opposing team?
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