Results 1 to 5 of 5

Math Help - Please Help ! Discrete Proof By Mathematical Induction.

  1. #1
    Newbie
    Joined
    Feb 2008
    Posts
    7

    Please Help ! Discrete Proof By Mathematical Induction.

    Prove that a set with n elements has n(n-1)(n-2)/6 subsets containing exactly three elements whenever n is an integer greater than or equal to 3.

    Please help, I understand the basics but I am currently stuck on this problem.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,394
    Thanks
    1476
    Awards
    1
    {\binom {n} {3}}=\frac{{n!}}{{\left( {3!} \right)\left( {n - 3} \right)!}} = \frac{{\left( n \right)\left( {n - 1} \right)\left( {n - 2} \right)\left( {n - 3} \right)!}}{{\left( {3!} \right)\left( {n - 3} \right)!}} = \frac{{\left( n \right)\left( {n - 1} \right)\left( {n - 2} \right)}}{{\left( 6 \right)}}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2008
    Posts
    7
    thanks, but it has to include a basis, induction hypothesis, and induction step for it be a complete proof.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,394
    Thanks
    1476
    Awards
    1
    Quote Originally Posted by jas05s View Post
    thanks, but it has to include a basis, induction hypothesis, and induction step for it be a complete proof.
    This is a prefect example of why many of us think that the current state of mathematics training is in the dumps. Given how many students have no clear idea what ‘induction proofs’ are all about, why complicate things with such a problem?
    Is this a set theory class? If it is then I am wrong.
    Otherwise, I stand by what I have written.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jan 2008
    Posts
    154
    Then base case: For  n = 3.... verify. Inductive step: For some integer  k , statement holds true.


    Prove that  P(k) \implies P(k+1) .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mathematical Induction Proof
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 8th 2010, 12:24 PM
  2. Proof by Mathematical Induction
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: February 28th 2010, 08:07 AM
  3. Proof by mathematical Induction
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: April 20th 2009, 07:33 AM
  4. Replies: 7
    Last Post: November 25th 2007, 10:31 AM
  5. Mathematical induction proof
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 13th 2007, 01:10 PM

Search Tags


/mathhelpforum @mathhelpforum