# Factorials

• November 2nd 2009, 10:15 AM
skeske1234
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

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?
• November 2nd 2009, 11:25 AM
craig

Quote:

Originally Posted by skeske1234
How many incorrect arrangements are there?

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.

Hope this helps
• November 2nd 2009, 11:32 AM
skeske1234
what do you mean when you say "only one of these" is the correct way?
• November 2nd 2009, 11:35 AM
craig
Well I presume that the correct arrangement would be volume 1,2,...12. This sequence only occurs once out of all 479,001,600, this would explain why the answer for the number of 'incorrect' ways is is 479,001,599.