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

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George C.
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Jan 21, 2017

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Put one of the two particular books to one side.

Then there are

There are

So there are:

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

ways to arrange the

Then you can place the reserved book on either side of its companion. So for each of the possible

So the number of acceptable arrangements of the

#8!*2 = 80640#

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