# in a party hall, 10 persons are to be arranged around a round table. if two particular persons are not to be seated side by side, then what is the total number of arrangements?

### Mohammed

Guys, does anyone know the answer?

get in a party hall, 10 persons are to be arranged around a round table. if two particular persons are not to be seated side by side, then what is the total number of arrangements? from screen.

## [Solved] 10 persons were invited to a party. In how many ways can the

Concept: The number of ways to arrange n distinct things in a circular arrangement is given by: (n – 1)! Calculation: After fixing the places of

Home Mathematics Permutations and Combinations

## Question

Download Solution PDF

## 10 persons were invited to a party. In how many ways can they be seated in a round table such that two particular persons sit on either side of the host?

8! × 2! 10! × 2! 9! × 2! 9! None of these

## Answer (Detailed Solution Below)

Option 1 : 8! × 2!

India's Super Teachers for all govt. exams Under One Roof

FREE

Demo Classes Available*

Enroll For Free Now

## Detailed Solution

Download Solution PDF

**Concept**:

The number of ways to arrange n distinct things in a **circular arrangement** is given by: (n – 1)!

**Calculation**:

After fixing the places of three persons (1 host + 2 persons) and treating them as 1 unit , so in total (10 – 2 + 1) = 9 units needs to be arranged in the round table.

Now, these 9 units can be arranged in a round table in (9 – 1)! = 8! ways.

Again these particular persons can sit on either side of the host in 2 ways.

Hence, the total number of ways to arrange these 10 persons in a round table = 8! × 2!

Download Solution PDF

Share on Whatsapp

Get proficient with the Mathematics concepts with detailed lessons on the topic Permutations and Combinations among many others.

India’s **#1 Learning** Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Get Started for Free

Download App

Trusted by 3,17,09,028+ Students

‹‹ Previous Ques Next Ques ››

## More Permutations and Combinations Questions

**Q1.**For a social work, 7 men and 6 women gave their nominations. The committee is formed to select 5 people from the nominated persons in such a way that atleast 3 men are there in the final team. Find the number of ways in which the people can be selected.

**Q2.**Evaluate

10P410C4 ?

**Q3.**Two digits out of 1, 2, 3, 4, 5 are chosen at random and multiplied together. What is the probability that the last digit in the product appears as 0?

**Q4.**What is the maximum value of n such that 5n divides (30! + 35!), where n is a natural number?

**Q5.**How many permutations are there of the letters of the word 'TIGER' in which the vowels should not occupy the even positions ?

**Q6.**How many odd numbers between 300 and 400 are there in which none of the digits is repeated ?

**Q7.**If C(3n, 2n) = C(3n, 2n - 7), then what is the value of C(n, n - 5)?

**Q8.**If 5P(4, n) = 6P(5, n - 1), then n is:-

**Q9.**In how many ways can a committee of 4 be made out of 5 men and 3 women containing at least one woman?

## 12 persons are to be arranged to a round table. If two particular persons among them are not to be side by side, the total number of arrangements is

Click here👆to get an answer to your question ✍️ 12 persons are to be arranged to a round table. If two particular persons among them are not to be side by side, the total number of arrangements is

Question

## 12 persons are to be arranged to a round table. If two particular persons among them are not to be side by side, the total number of arrangements is

**A**

## 9(10 !)

**B**

## 2(10 !)

**C**

## 45(8 !)

**D**

## 10 !

Hard Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is A)

Arrangements of 12 persons =11!2 persons can not seat together

=11!−10!2 10!(11−2)=9(10!)

Was this answer helpful?

41 2

## In how many ways can a party of 10 people be seated around a round table if certain 4 people refuse to sit next to each other?

Answer (1 of 2): In how many ways can a party of 10 people be seated around a round table if certain 4 people refuse to sit next to each other? Out of the 10, 6 people have no problem in sitting together. Let us call them friends. At a round table, these 6 friends can be seated in (6-1)! or 5! w...

In how many ways can a party of 10 people be seated around a round table if certain 4 people refuse to sit next to each other?

Ad by Amazon Web Services (AWS)

AWS is how.

AWS removes the complexity of building, training, and deploying machine learning models at any scale.

Sort Miyuki Nanase

Author has 1.3K answers and 108K answer viewsAug 5

Answer

= (10 — 4 — 1)! × (10 — 4)P4

= 5! × 6P4

= 120 × 6 × 5 × 4 × 3

= 720 × 60 = 43200 Related questions

10 people are seated on a round table. In how many ways can they be arranged if the two of them insist on sitting next to each other?

In how many ways can 7 people be seated at a round table, if two particular people must not sit next to each other?

How many ways can ten people be seated around a circular table if two people insist to sit next to each other?

In how many ways can 10 people be seated at a round table if two refused to seat together?

In how many ways can 10 people be seated on a bench if only 4 seat are available?

Sudhakar Babu DS

Puzzle EnthusiastAuthor has 387 answers and 854.2K answer views10mo

In how many ways can a party of 10 people be seated around a round table if certain 4 people refuse to sit next to each other?

Out of the 10, 6 people have no problem in sitting together. Let us call them friends. At a round table, these 6 friends can be seated in (6-1)! or 5! ways. Each of the remaining 4 persons (we call them foes), who refuse to be seated with each other, can be tucked in between any of the 6 pairs formed by the 6 friends. Say if ABCDEF is 1 seating arrangement of the 6 friends, out of the 5! arrangements, then there are 6 pairs of friends, namely AB,BC,CD,DE,EF and FA. We c

Miyuki Nanase

Author has 1.3K answers and 108K answer viewsAug 5

Related

In how many ways can 10 people take places at a round table if 3 people must not sit next to each other?

Answer = (7 — 1)! × 7P3

= 6! × 7! / (7 — 3)!

= 720 × 7 × 6 × 5 = 151200 Grammarly Sponsored

Communicate effectively throughout your writing universe.

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

Peter Butcher

MBA from Deakin University (Graduated 1998)Author has 1K answers and 2.6M answer views1y

Related

In how many ways can eight people be seated in a round table if two people insist in sitting next to each other?

In how many ways can eight people be seated in a round table if two people insist in sitting next to each other?

Initial Thoughts

I suspect this question isn't as difficult as it first looks!

Two people insist on being seated next to each other. The host could always tell them that they can't because the seating plan was arranged some time ago.

Each of the seats is equally spaced around the table and each seat is physically identical to every other seat.

Analysis

Sit Person 1 (one of the 2 who want to sit together) in any seat around the table. It doesn't matter which seat.

Thete are now 7 seats avai

K S Narayanan

Cost Accountant having 24 years Telecom ExperienceAuthor has 6K answers and 9.4M answer views4y

Related

In how many ways can 7 people be seated at a round table, if two particular people must not sit next to each other?

Number of ways in which 7 people can be seated around a round table without any condition is 6!.

Now, let us assume these two particular people ALWAYS sit together and let us consider them as one unit.

Number of ways in which 6 people can be arranged around a round table is 5! And the two particular peopke can be arranged betwern them selves in 2! = 2 ways.

Hence, number of ways in which 7 people can sit around a round table where the two people must not sit together is :

6! - (5! X 2) = 120 x 4 = 480

Artem Lensky

Fellow at Australian National University (2019–present)3y

Related

In how many ways can 5 men sit around a table solution?

Originally Answered: In how many ways can five students sit around a table?

There are five people and five seats. Hence, there are

5 5

ways to seat the first person,

4 4

ways to seat the second,

3 3

ways to seat the third,

2 2

ways to seat the fourth person and the firth person goes to the last remaining seat, so over there are

5! 5!

ways to seat five people.

Counting rotation equivalent seatings: What if we consider some of the seatings equivalent and the table is a round-table. For example, rotating people along the table clockwise or counterclockwise does not change their mutual position. Then, there are five possible actions that leave seatings equivalent, denote them by

{I, {I, USAFIS Sponsored

This is the best time to apply for the Green Card DV Lottery!

Get a chance to win and apply today! America is waiting for you with many amazing opportunities.

Doug Skilton

Enjoy recreational mathAuthor has 2.1K answers and 2.5M answer views3y

Related

How many ways can a group of 6 people be seated around a table if 2 of them insist on sitting beside each other?

1 of the 2 people who must sit together can choose any 1 of 6 places to sit. Because of the circular seating arrangement, the 6 choices collapse to just 1. The other 1 of the pair to be seated together then has 2 choices of seating in order that each sit together. the remaining 4 people can then be seated in 4! ways.

Guys, does anyone know the answer?

5