Factorial rules

[Takuya]

In my combinatorics book, it's discussing inclusion-exclusion, and it says that n!-(n-1)! = (n-1)!*(n-1)!

Can someone help me understand the rules of factorials? Thanks!

[deluks917]

The book has a mistake:

n! - (n-1)! = n * (n-1)! - (n-1)! = n * (n-1)! - 1 * (n-1)! = (n-1) * (n-1)!