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

1 Answer
Jan 21, 2017

Answer:

#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#