Results 1 to 3 of 3

Math Help - Binomial Coefficients

  1. #1
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    676
    Thanks
    19

    Binomial Coefficients

    Binomial coefficients are defined:

    \left(\begin{array}{c}n\\k\end{array}\right)=\frac  {n!}{k!(n-k)!}

    I'm not sure how two write these out going from k={0,1,2,...,n}. For k=0 I have:

    \left(\begin{array}{c}n\\0\end{array}\right)=\frac  {n!}{!(n-0)!}=\frac{n!}{1!n!}=\frac{n!}{n!}=1

    For k=1

    \left(\begin{array}{c}n\\1\end{array}\right)=\frac  {n!}{1!(n-1)!}=\frac{n!}{(n-1)!}

    I know this should equal n, but I don't know how to show that.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by adkinsjr View Post
    Binomial coefficients are defined:

    \left(\begin{array}{c}n\\k\end{array}\right)=\frac  {n!}{k!(n-k)!}

    I'm not sure how two write these out going from k={0,1,2,...,n}. For k=0 I have:

    \left(\begin{array}{c}n\\0\end{array}\right)=\frac  {n!}{!(n-0)!}=\frac{n!}{1!n!}=\frac{n!}{n!}=1

    For k=1

    \left(\begin{array}{c}n\\1\end{array}\right)=\frac  {n!}{1!(n-1)!}=\frac{n!}{(n-1)!}

    I know this should equal n, but I don't know how to show that.
    For the love's sake, n!=n\cdot(n-1)\cdots=n\cdot (n-1)!.
    Last edited by Plato; February 1st 2010 at 02:40 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    676
    Thanks
    19
    Ok, I wasn't aware of the formal definition of a factorial:

    n!=\left\{\begin{array}{cc}1,&\mbox{ if }<br />
n=0\\n(n-1)!, & \mbox{ if } n>0\end{array}\right.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Binomial coefficients?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 23rd 2009, 09:00 AM
  2. Binomial coefficients
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 25th 2009, 05:18 PM
  3. Binomial Coefficients
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 16th 2008, 07:04 AM
  4. Binomial coefficients
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: April 5th 2008, 11:21 AM
  5. Binomial Coefficients
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: July 23rd 2007, 10:47 AM

Search Tags


/mathhelpforum @mathhelpforum