Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A set of 7 distinct books needs to be arranged on a shelf. However, two specific books cannot be placed next to each other. In how many different ways can the books be ar

A set of 7 distinct books needs to be arranged on a shelf. However, two specific books cannot be placed next to each other. In how many different ways can the books be arranged in the shelf.

 

Option: 1

1250

 


Option: 2

1500

 


Option: 3

3600

 


Option: 4

2000


Answers (1)

best_answer

To calculate the number of different ways the 7 distinct books can be arranged on a shelf, with the condition that two specific books cannot be placed next to each other, we can use the concept of permutations.

First, let's consider the total number of arrangements without any restrictions. Since there are 7 distinct books, they can be arranged on the shelf in 7 ! (7 factorial) ways.

Next, let's consider the number of arrangements where the two specific books are placed next to each other. We can treat these two books as a single entity. Thus, we have 6 distinct entities to arrange on the shelf.

Since there are 6 distinct entities, they can be arranged in 6 ! ways.

However, within the arrangement of these 6 entities, the two specific books can be swapped. So, for each arrangement, there are 2 ! ( 2 factorial) ways to arrange the two specific books.

Therefore, the number of arrangements where the two specific books are placed next to each other is 6 ! \times 2 !.

To find the number of arrangements where the two specific books cannot be placed next to each other, we subtract the number of arrangements where the two specific books are placed next to each other from the total number of arrangements:

7 !-(6 ! \times 2 !)

Calculating this expression, we get:

7 !-(6 ! \times 2 !)=5,040-(720 \times 2)=5,040-1,440=3,600 .

Therefore, there are 3,600 different ways to arrange the 7 distinct books on the shelf, with the condition that two specific books cannot be placed next to each other.

Posted by

Riya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Mains 2025 Paper 2 Answer Key LIVE: BArch final answer key PDF at jeemain.nta.nic.in soon
anam-khan

JEE Main 2025 response sheet errors: Delhi HC allows student to apply for JEE Adv, seeks NTA explanation
anam-khan

Four Kashmiri girls defy the odds, score 99+ percentile in JEE Main 2025

Latest Question