Question

In how many ways can 9 books be arranged on a shelf if 2 of them must be kept together?

Answer 1

`8!*2 = 80640`

Explanation:

Put one of the two particular books to one side.

Then there are `8` books to arrange in any order on the shelf.

There are `8` choices for the first book, `7` for the next, `6` for the next, etc.

So there are:

`8! = 8 xx 7 xx 6 xx...xx 1 = 40320`

ways to arrange the `8` books.

Then you can place the reserved book on either side of its companion. So for each of the possible `40320` ways to arrange the other `8` books, there are `2` possible acceptable arrangements of `9` books.

So the number of acceptable arrangements of the `9` books is:

`8!*2 = 80640`