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

Jan 21, 2017

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