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Math Help - Inductive Proof: Permutations = Factorials

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    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?
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    MHF Contributor FernandoRevilla's Avatar
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    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 ...
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