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.
Question 1
1.
9!
Question 2
2.
7P5
Question 3
3.
7C5
Question 4
4.
( 8P3 ) ( 4P2 )
Question 5
5.
Enter your answer as a fraction in lowest terms:
6C3 / 8C5
Question 6
6.
10!
8!2!
Question 7
7.
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
Question 8
8.
Question 9
9.
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?
Question 10
10.
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.
Question 11
11.
Question 12
12.
Answer the question:
The ski club has ten members to choose two co-captains. How many ways can these positions be filled?
Question 13
13.
Question 14
14.
How many different ways can the word ELEMENTARY be arranged?
Question 15
15.
Question 16
16.
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?
Question 17
17.
Question 18
18.
Answer the question.
The batting order for eight players on a 10 person team.
Question 19
19.
Question 20
20.
Answer the question.
The student body of 125 students wants to elect a president, vice president, and secretary. How many possible results are there?
Question 21
21.
Question 22
22.
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?
Question 23
23.
Question 24
24.
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?
Question 25
25.
Question 26
26.
Answer the question.
The five Smith children run to the ice cream truck. How many ways can they line up to order?
Question 27
27.
Question 28
28.
Answer the question.
In how many ways can the letters in "market" be arranged?
Question 29
29.
Question 30
30.
Answer the question.
A volleyball squad has twelve players. How many ways can the players line up to greet the opposing team?
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
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
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
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
What kind of problem is this?
The batting order for eight players on a 10 person team.
combination
permutation
fundamental counting principle
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
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
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
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
What kind of problem is this?
In how many ways can the letters in "market" be arranged?
combination
permutation
fundamental counting principle
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?