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
But their answer is
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?