Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 416

A round table conference is to be held among 20 delegates of 20 countries. The no. of ways they can be seated if two particular delegates are never sit together is. (a) \(17 \cdot 18 !\) (b) \(18 \cdot 19 !\) (c) \((20 ! / 2)\) (d) \(19 ! \cdot 2\)

Short Answer

Expert verified
The correct answer is (b) \(18 \cdot 19 !\).

Step by step solution

01

Calculate the total number of ways to seat the delegates

First, let's find the total number of ways to seat the 20 delegates (without any restrictions). Since there are 20 seats, there are 20! (20 factorial) possible ways to arrange the delegates.
02

Calculate the number of ways in which the two particular delegates sit together

Now, we want to find the number of ways in which the two particular delegates sit together. We can treat them as a single unit (a "block") and then place the remaining 18 delegates. This will effectively make it 19 positions for the remaining 18 delegates and the block. So, there are 19! ways to arrange the delegates along with the block. However, within the block itself, there are 2! (or 2) ways to arrange the two particular delegates. Therefore, there are \(19! \cdot 2! \) ways where the two delegates sit together.
03

Calculate the number of ways in which the two particular delegates do NOT sit together

To find the number of ways in which the two delegates do NOT sit together, we will subtract the number of ways in which they sit together (from Step 2) from the total number of ways (from Step 1). So, the number of ways in which the two particular delegates do NOT sit together is: \( 20! - (19! \cdot 2!) \)
04

Simplify the expression

Now let's simplify this expression: \( 20! - (19! \cdot 2!) = 19! \cdot (20 - 2) = 19! \cdot 18\)
05

Identify the correct answer

The number of ways in which the two particular delegates do NOT sit together is \(19! \cdot 18\). This matches option (b) in the given choices. Therefore, the correct answer is (b) \(18 \cdot 19 !\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

If \({ }^{189} \mathrm{C}_{35}+{ }^{189} \mathrm{C}_{\mathrm{x}}={ }^{190} \mathrm{C}_{\mathrm{x}}\) then \(\mathrm{x}\) is equal to (a) 34 (b) 35 (c) 36 (d) 37

A class contain 4 boys and \(g\) girls every sunday 5 students including at least 3 boys go for a picnic to doll house, a different group being sent every week. During the picnic the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of \(g\) is (a) 15 (b) 12 (c) 8 (d) 5

The straight lines \(\mathrm{I}_{1}, \mathrm{I}_{2}, \mathrm{I}_{3}\) are parallel and lie in the same plane. A total number of \(m\) points are taken on \(I_{1}, n\) points on \(\mathrm{I}_{2}, \mathrm{k}\) points on \(\mathrm{I}_{3}\). The maximum number of triangles formed with vertices at these points are (a) \(^{\mathrm{m}+\mathrm{n}+\mathrm{k}} \mathrm{C}_{3}\) (b) \({ }^{\mathrm{m}+\mathrm{n}+\overline{\mathrm{k}} \mathrm{C}_{3}-{ }^{\mathrm{m}}} \mathrm{C}_{3}-{ }^{\mathrm{n}} \mathrm{C}_{3}-{ }^{\mathrm{k}} \mathrm{C}_{3}\) (c) \({ }^{\mathrm{m}} \mathrm{C}_{3}+{ }^{\mathrm{n}} \mathrm{C}_{3}+{ }^{\mathrm{k}} \mathrm{C}_{3}\) (d) \(m+n+k-{ }^{m+n+k} C_{3}\)

In a circus there are 10 cages for accommodating 10 animals out of these 4 cages are so small that five out of ten animals can not enter into them. In how many ways will it be possible to accommodate 10 animals in these 10 cages? (a) 66400 (b) 86400 (c) 96400 (d) 46900

The number of ways in which a committee of 3 women and 4 men be chosen from 8 women and 7 men is formed if \(\mathrm{mr}\). \(\mathrm{A}\) refuses to serve on the committee if \(\mathrm{mr}\). \(\mathrm{B}\) is a member of the committee is (a) 420 (b) 840 (c) 1540 (d) none of these
See all solutions

Recommended explanations on English Textbooks

Language Analysis

Read Explanation

Key Concepts in Language and Linguistics

Read Explanation

Synthesis Essay

Read Explanation

Cues and Conventions

Read Explanation

Discourse

Read Explanation

Email

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free