### Instruction: In how many ways can I arrange four different books on a shelf?### Response: To arrange four books, I need to choose which one goes in the first position, then the second, then the third, and then the fourth.
For the first position, I have four choices, since any of the books can go there.
For the second position, I have three choices, since I can't repeat the book I already put in the first position.
For the third position, I have two choices, since I can't repeat the books I already put in the first and second positions.
For the fourth position, I have one choice, since there is only one book left.
So the total number of ways to arrange four books is 4 x 3 x 2 x 1, which is also called 4 factorial and written as 4!.
I can use a calculator or do the multiplication by hand to get 4! = 4 x 3 x 2 x 1 = 24.