# How many ways can 3 dictionaries and 5 magazines be arranged on a shelf if there must be a dictionary on each end?

$8 , 640$

#### Explanation:

There are different ways to calculate something like this. Let me walk you through the way I approach this:

We have 8 things in total - 3 dictionaries and 5 magazines. There must be a dictionary on each end.

So let's talk about the ends first. The first end can be any 1 of 3 dictionaries and so that is 3!

Next we have the other end which also must be a dictionary so that gives us another 2!

Now we can arrange the remaining 5 magazines and 1 dictionary, so 6 items in total (this is a permutation calculation):

P_(6,6)=(6!)/((6-6)!)=(6!)/(0!)=(6!)/1=720

All in all, we have:

3!xx2!xx720=6xx2xx720=8,640