Factorial rules (1 Viewer)

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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!
The book has a mistake:

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

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