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

### Mohammed

Guys, does anyone know the answer?

get in how many different ways can six friends sit for a photograph of five chairs in a row? from screen.

## 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

3.2 Answer: 3.3 Part 2

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

3.5 Answer: 3.6 Part 3

3.7 Permutation when the repetition of the words are allowed

3.8 Answer: 3.9 Part 4

3.10 Different Types of Arrangement

3.11 Answer:

**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

### Answer:

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

### Part 2

### 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

### Answer:

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

### Part 3

### 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?

## 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

Forum Home GMAT Quantitative

Problem Solving (PS)

Unanswered Active Topics Register GMAT Club Tests Decision Tracker My Rewards New posts New comers' posts

🔴 **Live on YouTube**** - ****Learn the Ultimate Core Skill to Crush GMAT Critical Reasoning**

## EVENTS & PROMOTIONS

Nov

**24**

All GMAT Club Tests are free and open on Thursday, November 24th, in celebration of Thanksgiving Day

Nov

**23**

Learn the Ultimate Core Skill to Crush GMAT Critical Reasoning | GMAT Verbal

Nov

**24**

Harrison's Journey to a GMAT 760 Score

Nov

**24**

Deferred Applicant with SIA Admissions

Nov

**25**

Shubhankar Scored 760 (Q50/V42) on the GMAT Using TTP's Accelerated Study Plan.

Nov

**25**

Free full-length test!

Nov

**26**

Timing & Test Taking Strategy to score 750+ on GMAT (Live Webinar)

Nov

**26**

Free GMAT CR Webinar

Nov

**26**

All GMAT Practice tests at just $14.95

Nov

**27**

The Art of Involved and Evolved Reading for RC (Live Webinar)

Nov

**27**

Master 700-level PS and DS Questions using the Remainder Equation

Nov

**27**

Q&A with ISB Adcom | Hosted by Experts' Global

Nov

**28**

Magoosh Black Friday Sale

Save Now! Nov

**28**

### Magoosh Black Friday Sale

08:00 PM PST - 11:00 PM PST

This month save 30% on GMAT prep plans with the code BLACKFRI30GMAT during our Black Friday sale from Tuesday, 11/22 to Monday, 11/28.

Learn More Nov

**24**

### All GMAT Club Tests are free and open on Thursday, November 24th, in celebration of Thanksgiving Day

12:01 AM PST - 11:59 PM PST

This Thursday, GMAT Club Tests will be Absolutely Free! Including all the Quizzes, Questions, and Tests. 12 AM - 11:59 PM PDT

Set a Reminder Nov

**23**

### Learn the Ultimate Core Skill to Crush GMAT Critical Reasoning | GMAT Verbal

07:30 AM PST - 08:30 AM PST

Have you ever wondered why some folks ace GMAT Critical Reasoning with minimal effort, whereas some others practice, practice, and then practice some more without really seeing much improvement? Why does such a difference exist?

Learn More Nov

**24**

### Harrison's Journey to a GMAT 760 Score

12:00 PM EST - 01:00 PM EST

Learn how Harrison achieved a 760 on the GMAT using Target Test Prep's Structured Study Plan.

Join the Chat Nov

**24**

### Deferred Applicant with SIA Admissions

09:30 PM IST - 10:00 PM IST

Join us Live on GMAT Club's Instagram with Susan Bershaj Founder and CEO of SIA Admissions. She will be discussing Deferred Applicants.

Learn More Nov

**25**

### Shubhankar Scored 760 (Q50/V42) on the GMAT Using TTP's Accelerated Study Plan.

03:00 PM EST - 04:00 PM EST

Shubhankar studied for 6 more weeks using TTP’s Accelerated Study Plan, and on test day, he finally got the improvement he’d been seeking, scoring 760, his GMAT goal.

Learn More Nov

**25**

### Free full-length test!

08:00 PM PST - 09:00 PM PST

Video explanations + diagnosis of 10 weakest areas + one-week access to 10 SC e-books and 200 short videos!

Register Now Nov

**26**

### Timing & Test Taking Strategy to score 750+ on GMAT (Live Webinar)

05:30 AM PST - 07:30 AM PST

Many students have a tough time understanding how the GMAT algorithm works and hence, fail to fine-tune their preparation to get the maximum out of it. Learn how to decode the algorithm and modify your prep strategy to score GMAT 750+!

Register for Free Nov

**26**

### Free GMAT CR Webinar

07:00 AM PST - 09:00 AM PST

Attend this webinar to learn two proprietary ways to Pre-Think assumptions and ace GMAT CR in 10 days.

Learn More Nov

**26**

### All GMAT Practice tests at just $14.95

08:00 PM PST - 09:00 PM PST

Use this Black Friday to make your GMAT prep BRIGHTER. Use Code - GMATBFCM to get any individual practice test at just $14.95.

Register for Free Nov

**27**

### The Art of Involved and Evolved Reading for RC (Live Webinar)

05:30 AM PST - 07:30 AM PST

Did you know 85% of the RC questions are inference based? Learn the Art of Involved & Evolved Reading and make sure you never get an RC question wrong again!

Register Now Nov

**27**

### Master 700-level PS and DS Questions using the Remainder Equation

07:00 AM PST - 09:00 AM PST

Attend this webinar to learn the core NP concepts and a structured approach to solve 700+ Number Properties questions in less than 2 minutes.

Register Nov

**27**

### Q&A with ISB Adcom | Hosted by Experts' Global

06:00 PM IST - 07:30 PM IST

Ask Me Anything session with ISB Admissions Team • How to build a Strong application to ISB • Know more about Holistic Evaluation at ISB - The weightage assigned to different aspects of your profile and more.

Save Now! Nov

**28**

### Magoosh Black Friday Sale

08:00 PM PST - 11:00 PM PST

This month save 30% on GMAT prep plans with the code BLACKFRI30GMAT during our Black Friday sale from Tuesday, 11/22 to Monday, 11/28.

## 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?

Ad by Amazon Web Services (AWS)

Build low-cost web applications with AWS.

You can use whatever CMS you like, including WordPress, Drupal, and more. Get started for free.

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.

Related questions

In how many ways can 5 people be seated in a row of 9 chairs?

In how many ways can you seat 5 people out of 10 in a row of 5 chairs?

In how many ways can 5 people sit in 5 chairs such that "Person A" doesn't seat next to "Person B"?

In how many different ways can 6 people be seated in 10 seats?

How many ways can 5 people line up?

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

Sponsored by Aspose

.NET Microsoft OneNote documents processing APIs.

Create, manipulate and convert OneNote files to multiple formats using C# API.

Saad Salman 4y

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

Author has 13.4K answers and 5.8M answer viewsMay 16, 2021

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

Related questions

In how many ways can 5 students be seated in a row of 7 chairs if two of them insist on sitting next to each other?

How many different ways can 7 people sit on 9 different chairs?

How many ways can five students be seated in a row of two chairs?

In how many ways can 4 students be seated in a row of 20 chairs?

In how many ways can 5 students be seated in a row of 5 seats if 2 of the students insist on sitting besides each other?

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

Sponsored by Grammarly

Communicate effectively throughout your writing universe.

Grammarly for Windows and Mac offers writing feedback in Slack, Word, Gmail, and beyond. Install it now!

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

Sponsored by Nokia

Your cloud-based solution for 5G network protection.

Automate security against cyber threats with Nokia NetGuard Cybersecurity Dome.

Lets Learn Aptitude Answered by Vikas Dhiman

Author has 107 answers and 76.9K answer viewsMay 23, 2021

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

Author has 67 answers and 29.1K answer viewsMay 16, 2021

Guys, does anyone know the answer?