# Math Help - Factorials

1. ## Factorials

A 12-volume encyclopedia is to be placed on a shelf. How many incorrect arrangements are there?

This is my work:

12!=479 001 600

12! - 1 =479 001 599

My question: Why did they subtract 1 from 12! ?

I know that 12! means how many possible ways you can arrange them correctly, but why subtract 1 for incorrect ways? Could you use any number to subtract away from 12! ? and then that would be considered incorrect?

Your actual working out is correct, there are $12!$ ways to arrange them. However, only one of these is the correct way, hence the subtract one.