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# in how many different ways can six friends sit for a photograph of five chairs in a row?

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## Permutation and Combination Practice Questions: Questions & Answers

Permutation and combination is a very important topic in any competitive exams. We have covered this topic and all its sections in our earlier articles. Today we are going to discuss the permutation and combination practice questions.

Permutation and Combination

## Permutation and Combination Practice Questions

Permutation and combination is a very important topic in any competitive exams. We have covered this topic and all its sections in our earlier articles. Today we are going to discuss the permutation and combination practice questions. There are different types of practice questions for you to practice and get ready for the competitive exams.

Table of content

1 Browse more Topics under Permutation And Combination

2 Permutation and Combination Practice Questions

3 Part 1

3.1 Permutation of ‘x’ things using all of them

3.4 Permutations of n things taking some of them at one time and when some things are alike

3.7 Permutation when the repetition of the words are allowed

3.10 Different Types of Arrangement

### Browse more Topics under Permutation And Combination

Factorial Notation Permutations

Number of Permutations

Combination

Number of Combination

## Permutation and Combination Practice Questions

Permutation and Combination Practice Questions Part 1

### Permutation of ‘x’ things using all of them

Directions: For the questions in the section you need to find the distinctive ways to find the answer.

1. Using all the letters of the word GIFT how many distinct words can be formed?

A. 22 words            B. 24 words        C. 256 words       D. 200 words

2. Find out how many distinct three-digit numbers can be formed using all the digits of 1, 2, and 3.

A. 4            B. 5           C. 6              D. 7

3. In how many different ways can five friends sit for a photograph of five chairs in a row?

A. 120 ways       B. 24 ways         C. 240 ways            D. 720 ways

4. In how many different ways can the letters of the word MAGIC can be formed?

A. 24 ways           B. 120 ways           C. 240 ways              D. 720 ways

5. For the above word how many different types of arrangement are possible so that the vowels are always together?

A. 44 words       B. 24 words            C. 48 words           D. 60 words

6. In how many ways can the letters of the word BEAUTY be arranged?

A. 360           B. 5!           C. 6!             D. 7!

7. For the above word, if the vowels are always together than how many types of arrangement can be possible?

A. 4! * 3!       B. 6!        C. 4!           D. 4! * 3

8. A person has 4 coins if different denominations. What is the number of different sums of money the person can form?

A. 12        B. 15              C. 11             D. 16

1. B 24 2. C 6 3. A  120 ways 4. B 120 ways 5. C 48 words 6. C 6! 7. A 4! * 3! 8. B 15

### Permutations of n things taking some of them at one time and when some things are alike

Directions: Answer the questions based on the data given to you

1. If repetition is not allowed then how many distinct three-digit numbers can be formed using the digits (1, 2, 3, 4, 5)?

A. 60 ways          B. 50 ways              C. 40 ways           D. 30 ways

2. Find out the distinct four-letter words that can be formed using the word SINGAPORE.

A. 256       B. 1024            C. 3024            D. 2048

3. Find out how many distinct three-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 such that the digits are in ascending order.

A. 80          B. 81              C. 83            D. 84

4. How many can 3 digits be formed using the digits from 1 to 5 if the digit 2 is never there in the number?

A. 24           B. 36         C. 40            D. 52

5. If no repetition is not allowed then how many numbers between 2000 and 3000 can be formed using the digits from 0 to 7?

A. 42             B. 336             C. 210              D. 440

6. In how many ways can Kamal choose a consonant and a vowel from the letters of the word ALLAHABAD?

A. 4             B. 5              C. 6           D. 9

7. Find out the number of distinctive words that can be formed using the word GOOD.

A. 16          B. 24             C. 28           D. 48

8. How many different words can be formed from the alphabets of the word SCISSORS?

A. 1440         B. 1680               C. 1800             D. 2100

9. How many distinct words can be formed using the word MINIMUM?

A. 420           B. 450            C. 1024            D. 1048

1. A 60 ways 2. C 3024 3. D 84 4. A 24 5. C 210 6. A 4 7. B 24 8. B 1680 9. A 420

### Permutation when the repetition of the words are allowed

Directions: The questions in this section consists of the repetition of the words or letters or numbers or alphabets.

1. If repetition is allowed then how many different three digits numbers can be formed using the digits from 1 to 5?

A. 125         B. 27          C. 120           D. None of the above

2. In how many ways can two letters be selected from the English alphabet if repetition is allowed?

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## How many ways can six friends be arranged around a circular dinner tab : Problem Solving (PS)

How many ways can six friends be arranged around a circular dinner table? A. 16 B. 48 C. 96 D. 120 E. 720

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## In how many ways can you seat 5 people in a row of 5 chairs?

Answer (1 of 14): 5! No, I'm not particularly excited about this answer. That exclamation point, when used in mathematics, is called a factorial. It tells you to take the number in front of it, in this case 5, and multiply it by every digit smaller than it until you get to 1. So 5! = 5x4x3x2x1 =...

In how many ways can you seat 5 people in a row of 5 chairs?

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Sort Andre Engels

M.A. in Mathematics & Physics (college minor), University of Groningen (Graduated 1996)Author has 2.6K answers and 1.3M answer views5y

There are 5 different possibilities for seating someone on the first chair. Next there are 4 possibilities left for seating someone on the second chair. Thus there are in total 5x4=20 possibilities to fill the first two chairs. Likewise, there are 3 possibilities for the third chair, 2 for the fourth and finally only 1 for the last chair (the person that is left), giving us 5x4x3x2x1=120 possibilities altogether.

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Trenton Rosenquist

M.S. in Physics, San Francisco State University (SFSU) (Graduated 2020)4y

5!

No, I'm not particularly excited about this answer. That exclamation point, when used in mathematics, is called a factorial. It tells you to take the number in front of it, in this case 5, and multiply it by every digit smaller than it until you get to 1. So 5! = 5x4x3x2x1 = 120.

How did I get that answer? Well, imagine that you have your five empty chairs in front of you waiting to do what they do best: seat people.

\__/ \__/ \__/ \__/ \__/

Now, let's say there are 5 people named Alice, Bob, Charlie, Damon, and Eliza (who all like to go by their first initial), and they all want to have a seat

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According to a chapter of Mathematics knows as Permutation, its quite simple… Put in the calculator 5 factorial that is 5 x 4 x 3 x 2 x 1 and the answer is 120..

So there are 120 different ways to do it

Lets Learn Aptitude Answered by Jayanta Mukherjee

It is a case of permutation of 5 persons in a row; so, the answer will be (5!) = 120.

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Peter Keusgen

Former Oil and Energy AnalystAuthor has 708 answers and 185.4K answer viewsApr 4

The number of permutations depends only on your imagination.

Using the base of 5, you can add crossed arms, crossed legs, facing NSWE, different locations, different spacings, and even different times.

The total so far should be in the realm of 20!

So the effective answer depends on how much time you have to sit these people down in a row. In most countries I’d say it would be about five minutes before they revolted. In Asia as a teacher you could probably make a game of it and get to half an hour. The best would be the Chinese Communist Party which, judging by the lockdown in Shanghai, could go

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Roger Pickering

First class degree mathematics.Author has 9.7K answers and 3.2M answer viewsUpdated Jan 23

I have a somewhat different conclusion than others who have answered this question.

Yes on the face of it, there are 120 ways of seating the five people. But the arrangement A-B-C-D-E is essentially the same as E-D-C-B-A because each person has exactly the same person or persons next to them (admittedly with left replacing right).

Anyway my conclusion is that in this sense, of how many neighbours each person has, and who are those neighbours, there are 60 ways of seating the five people.

Bhatt Nandish

Finance Executive at Ishan Netsol (Indian company) (2017–present)4y

The number of people as well as the number of chairs is 5. Therefore, the number of ways in which 5 people can be seated = Therefore, there are exactly 120 ways in which they can be seated.5chair =5! 1*2*3*4*5=120ways

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Lets Learn Aptitude Answered by Vikas Dhiman

We have 5 people as well as 5 chairs

So the number of seating arrangement = 5c5×5! = 1×5! = 120

Lets Learn Aptitude Answered by Keerthi Goudnaik