Counting Principle And Permutation Quiz

Approved & Edited by ProProfs Editorial Team

The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.

Learn about Our Editorial Process

| By Salgm

Salgm

Community Contributor

Quizzes Created: 5 | Total Attempts: 3,720

Questions: 10 | Attempts: 2,676 | Updated: Jan 24, 2024

Questions

Settings

Feedback

During the Quiz End of Quiz

Difficulty

Sequential Easy First Hard First

Play as

Quiz Flashcard

Create your own Quiz

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

Counting Principle And Permutation Quiz - Quiz

Prepare yourself to take this counting principle and permutation quiz. The Fundamental Counting Principle says that if one event has 'k' possible outcomes and another event has 'n' possible outcomes, then there have to be "k ⋅ n" total possible outcomes for those two events together. A permutation is known as an arrangement of objects in a definite order. Attempt these questions to test and enhance your skills even more. Good luck!

Questions and Answers

1.

How many ways can 10 students win a race?
- A.
  
  2
- B.
  
  5
- C.
  
  10
- D.
  
  13
Correct Answer
C. 10

Explanation
There are 10 students participating in the race, and each student has a chance of winning. Therefore, there are 10 possible ways in which the students can win the race.

Rate this question:

2
0
2.

How many ways can I arrange 5 books?
- A.
  
  5 ways
- B.
  
  10 ways
- C.
  
  120 ways
- D.
  
  150 ways
Correct Answer
C. 120 ways

Explanation
The number of ways to arrange 5 books can be calculated using the concept of permutations. Since the order of arrangement matters, we can use the formula for permutations of n objects taken r at a time, which is n! / (n-r)!. In this case, we have 5 books to arrange, so the formula becomes 5! / (5-5)! = 5! / 0! = 5! = 5 x 4 x 3 x 2 x 1 = 120 ways. Therefore, the correct answer is 120 ways.

Rate this question:

3
0
3.

I can choose a red, blue, or green T-shirt, with a skirt or pants, a black, white, or green hijab, with or without a jacket. How many different choices do I have?
- A.
  
  3 x 2 x 3 x 2
- B.
  
  3 x 1 x 2 x 3
- C.
  
  3 x 3x 0 x 1
- D.
  
  4 x 9 x 5x 3
Correct Answer
A. 3 x 2 x 3 x 2

Explanation
There are 3 choices for the color of the T-shirt (red, blue, or green), 2 choices for the type of bottom (skirt or pants), 3 choices for the color of the hijab (black, white, or green), and 2 choices for whether or not to wear a jacket. Therefore, the total number of different choices is calculated by multiplying these numbers together: 3 x 2 x 3 x 2 = 36.

Rate this question:

3
0
4.

How many ways can we arrange 7 people sitting on 3 chairs?
- A.
  
  112
- B.
  
  157
- C.
  
  173
- D.
  
  210
Correct Answer
D. 210

Explanation
There are 7 people and 3 chairs available. The first person has 7 options to choose from, the second person has 6 options remaining, and the third person has 5 options left. Therefore, the total number of ways to arrange the 7 people on 3 chairs is 7 x 6 x 5 = 210.

Rate this question:

2
0
5.

How many ways can I arrange the letters of the word FLORIDA?
- A.
  
  5010
- B.
  
  5020
- C.
  
  5040
- D.
  
  5060
Correct Answer
C. 5040

Explanation
To find the number of ways to arrange the letters in the word "FLORIDA," we consider the total number of arrangements, which is 7 factorial (7!). This means multiplying 7 by each decreasing positive integer down to 1.
So, it's like calculating 7 times 6 times 5 times 4 times 3 times 2 times 1, which equals 5040. Therefore, there are 5040 different ways you can arrange the letters in the word "FLORIDA."

Rate this question:

1
0
6.

How many different license plates are possible if the first two places are numbers and the last two are letters, with repeating numbers or letters?
- A.
  
  92942
- B.
  
  29823
- C.
  
  57291
- D.
  
  67600
Correct Answer
D. 67600

Explanation
The given answer, 67600, is the number of different license plates that are possible if the first two places are numbers and the last two are letters, with repeating numbers or letters. This can be calculated by multiplying the number of possibilities for each place. For the first two places as numbers, there are 10 options (0-9). For the last two places as letters, there are 26 options (A-Z). Since repetition is allowed, the total number of possibilities is 10 * 10 * 26 * 26 = 67600.

Rate this question:

3
0
7.

Evaluate P(5,3)
- A.
  
  20
- B.
  
  60
- C.
  
  57
- D.
  
  82
Correct Answer
B. 60

Explanation
The question is asking to evaluate the permutation of 5 objects taken 3 at a time. The formula for evaluating permutations is P(n,r) = n! / (n-r)!. In this case, P(5,3) = 5! / (5-3)! = 5! / 2! = 5 x 4 x 3 / 2 x 1 = 60. Therefore, the correct answer is 60.

Rate this question:

1
0
8.

A briefcase lock has 3 rotating cylinders, each containing 10 digits. How many numerical codes are possible?
- A.
  
  10
- B.
  
  30
- C.
  
  1000
- D.
  
  1200
Correct Answer
C. 1000

Explanation
Each cylinder can be set to any of the 10 digits, so there are 10 options for each cylinder. Since there are 3 cylinders, the total number of possible combinations is 10 x 10 x 10 = 1000.

Rate this question:

3
0
9.

From 15 entries in an art contest, a camp counselor chooses first, second, and third place winners. How many choices can be made?
- A.
  
  2730
- B.
  
  15
- C.
  
  45
- D.
  
  8210
Correct Answer
A. 2730

Explanation
There are 15 choices for the first place winner, then 14 choices remaining for the second place winner, and 13 choices remaining for the third place winner. Therefore, the total number of choices that can be made is 15 * 14 * 13 = 2730.

Rate this question:

1
0
10.

How many 6-character passwords can be formed if the first character is a digit and the remaining 5 characters are letters that can be repeated?
- A.
  
  10x26x25x24x23x22
- B.
  
  10x26x26x26x26x26
- C.
  
  10x26!
- D.
  
  260
Correct Answer
B. 10x26x26x26x26x26

Explanation
The question asks for the number of 6-character passwords that can be formed. The first character must be a digit, which gives us 10 choices (0-9). The remaining 5 characters can be any letter, which gives us 26 choices for each character. Since the letters can be repeated, we multiply the choices together: 10x26x26x26x26x26. This gives us the total number of possible passwords that can be formed.

Rate this question:

1
0

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

Current Version
Jan 24, 2024

Quiz Edited by
ProProfs Editorial Team
May 12, 2010

Quiz Created by
Salgm

Counting Principle And Permutation Quiz

How many ways can 10 students win a race?

How many ways can I arrange 5 books?

I can choose a red, blue, or green T-shirt, with a skirt or pants, a black, white, or green hijab, with or without a jacket. How many different choices do I have?

How many ways can we arrange 7 people sitting on 3 chairs?

How many ways can I arrange the letters of the word FLORIDA?

How many different license plates are possible if the first two places are numbers and the last two are letters, with repeating numbers or letters?

Evaluate P(5,3)

A briefcase lock has 3 rotating cylinders, each containing 10 digits. How many numerical codes are possible?

From 15 entries in an art contest, a camp counselor chooses first, second, and third place winners. How many choices can be made?

How many 6-character passwords can be formed if the first character is a digit and the remaining 5 characters are letters that can be repeated?