Mary has 8 pairs of dress shoes. How many different ways can she arrange five pairs of her shoes in her closet?
For the first pair (on the left) there are 8 choices.
For the second pair, there are 7 pairs from which to choose.
....
For the fifth and last pair (which she puts on the right), there are 4 choices.
The number of ways to choose (and to arrange) is therefore the product of all the number of choices
8*7*...*4 = 8!/(8-5)! = 8!/3!