Results 1 to 2 of 2

Thread: Inductive Proof: Permutations = Factorials

  1. #1
    Member
    Joined
    Aug 2011
    Posts
    78
    Thanks
    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?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,163
    Thanks
    46

    Re: Inductive Proof: Permutations = Factorials

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

    Induction step: Suppose that for $\displaystyle n-1$ objects $\displaystyle (n\geq 2)$ we have $\displaystyle (n-1)!$ permutations then ...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inductive Proof
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: May 16th 2010, 08:57 PM
  2. Factorials, Combinations, Permutations & Probability
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: Apr 7th 2009, 09:21 AM
  3. permutations and factorials
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: Feb 8th 2009, 02:04 PM
  4. Permutations & Factorials
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: Jul 3rd 2008, 08:02 PM
  5. help...inductive proof???
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Feb 16th 2008, 03:11 PM

Search tags for this page

Search Tags


/mathhelpforum @mathhelpforum