Results 1 to 2 of 2

Math Help - combinatorics: binomial coefficients

  1. #1
    Member
    Joined
    Oct 2007
    Posts
    89

    combinatorics: binomial coefficients

    Hello.
    I am looking for advice for the following question.

    Find all values of n and k for which C(n, k+1) = 3*C(n, k)

    Would I convert the equation into factorials using C(n, k) = n! / (k)!(n-k)!
    Or is there something simpler that I am just not seeing
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by chrisc View Post
    Hello.
    I am looking for advice for the following question.

    Find all values of n and k for which C(n, k+1) = 3*C(n, k)

    Would I convert the equation into factorials using C(n, k) = n! / (k)!(n-k)!
    Or is there something simpler that I am just not seeing
    hi Chris,

    You do have a choice here....

    \displaystyle\binom{n}{k+1}=3\binom{n}{k}\Rightarr  ow\frac{n!}{(n-k-1)!(k+1)!}=3\frac{n!}{(n-k)!k!}

    \displaystyle\Rightarrow\frac{n!}{(n-k-1)!(k+1)k!}=3\frac{n!}{(n-k)(n-k-1)!k!}

    which allows you to simplify and find the relationship between n and k.


    Alternatively, you could use the following identity, though there is little point!!

    \displaystyle\binom{n}{k}+\binom{n}{k+1}=\binom{n+  1}{k+1}

    \displaystyle\binom{n}{k+1}=3\binom{n}{k}\Rightarr  ow\ 3\binom{n}{k}=\binom{n+1}{k+1}-\binom{n}{k}

    \displaystyle\ 4\binom{n}{k}=\binom{n+1}{k+1}

    which, simplified leads to the same relationship.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Combinatorics & Binomial Probability
    Posted in the Statistics Forum
    Replies: 4
    Last Post: November 8th 2011, 09:28 PM
  2. Combinatorics(Binomial Coefficients)?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 25th 2009, 10:39 PM
  3. Binomial coefficients
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 13th 2009, 12:22 PM
  4. Binomial Coefficients
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 16th 2008, 07:04 AM
  5. Binomial Coefficients Help
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 31st 2007, 06:34 AM

Search Tags


/mathhelpforum @mathhelpforum