Question

In how many way n books can be arranged so that two particular books are not together

Answer 1

Books are arranged in shelf.

Final Answer : (n-1)! (n-2)

Steps:
1) Total no. of ways in which 'n' can be arranged in shelf = n!

2) Now, we will find out the number of ways in which 'n' books can be arranged in a shelf such that particular pair of books will always together .

Here,
We will consider two books as single book .
Total no. of books become = (n-1) .
The (n-1) books can be arranged in (n-1)! .
We considered two books together, which themselves can be arranged in 2! ways.

3) No. of ways in which particular books are together = (n-1)! x 2 ! .

4) Finally,
No. of ways in which 'n' books can be arranged in a shelf such that no two books are together = n! - (n-1)! x 2!
= n(n-1)! -(n-1)!x2
= (n-2) (n-1)!.