Free help with homework

Why join Brainly?

  • ask questions about your assignment
  • get answers with explanations
  • find similar questions

In how many ways can 7 different books be arranged in a shelf ? in how many ways can we arrange three particular books so that they are always together?



1) If any arrangement is possible, there are 7! = 5040
So there are 5040 ways to arrange 7 books on a shelf.

2) If 3 particular books must always stand together, the 3 books can occupy the following positions on the shelf:


For each of these five cases, there are 3! permutations of the 3 books and 4! permutations of the other 4 books,
so the total number of allowed arrangements is 5 x 3!4! = 720.

1 5 1
Consider 3 particular books as 1 unit 
 1 unit +remaining 4 books=5
these 5 can be placed in 120 ways   

0 0 0
The Brain
  • The Brain
  • Helper
Not sure about the answer?
Learn more with Brainly!
Having trouble with your homework?
Get free help!
  • 80% of questions are answered in under 10 minutes
  • Answers come with explanations, so that you can learn
  • Answer quality is ensured by our experts