How many ways can 4 DVDs be arranged on a shelf?

Solution:

There are 4 ways to choose the first DVD, 3 ways to choose the second, 2 ways to choose the third and 1 way to choose the last. In other words, there are 4 x 3 x 2 x 1 = 4! =24 ways to arrange the DVDs.

Example: How many ways can John, Katherine, Luke, Melanie and Nick sit at a table?

Solution: The number of ways to arrange these five people is 5!

5! = 5 x 4 x 3 x 2 x 1 = 120. There are 120 permutations.

Example: How many ways can n objects be arranged?

Solution: n objects can be arranged in n! ways.