Math Help - Inductive Proof: Permutations = Factorials

1. Inductive Proof: Permutations = Factorials

Hi. I have this practice problem (not-graded) in a chapter concerning inductive proofs:

Prove that for any natural number n, there are exactly n! permutations of n objects.
I believe I understand the four steps of mathematical induction and can solve this, but I'm having trouble getting started: i.e., formulating the equation to be proved. Could someone point me in the right direction?

2. Re: Inductive Proof: Permutations = Factorials

Basis step: For $n=1$ we have only one object ( $a_1$) and only one permutation: $a_1$ i.e. we have $1=1!$ permutations.

Induction step: Suppose that for $n-1$ objects $(n\geq 2)$ we have $(n-1)!$ permutations then ...