How many different ways could you arrange four books on a shelf

There are 24 different ways you could arrange four books on a shelf.

This can be calculated using the formula for permutations which is n! / (n-k)! where n is the number of objects to choose from and k is the number of objects to choose.

In this case, n is 4 (the number of books) and k is also 4 (since we are arranging all four books).

So the calculation would be:

4! / (4-4)! = 4! / 0! = 24

This means there are 24 different ways to arrange the books on the shelf.