Notices
Results 1 to 5 of 5

Thread: binomial coefficients

  1. #1 binomial coefficients 
    Forum Ph.D.
    Join Date
    Dec 2006
    Location
    Norway
    Posts
    927
    i tried to understand what the binomial coefficient is. and i brutally failed.

    http://www.mathwords.com/b/binomial_coefficients.htm

    this webpage which usually is pretty helpful.. well it confused me even further.


    when you have eliminated the impossible, whatever remains, however improbable, must be the truth
    A.C Doyle
    Reply With Quote  
     

  2.  
     

  3. #2 Re: binomial coefficients 
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by dejawolf
    i tried to understand what the binomial coefficient is. and i brutally failed.

    http://www.mathwords.com/b/binomial_coefficients.htm

    this webpage which usually is pretty helpful.. well it confused me even further.
    Do you have a specific question?

    Here is a general explanation http://en.wikipedia.org/wiki/Binomial_coefficient
    and another http://mathworld.wolfram.com/BinomialCoefficient.html


    Reply With Quote  
     

  4. #3 Re: binomial coefficients 
    Forum Ph.D.
    Join Date
    Dec 2006
    Location
    Norway
    Posts
    927
    Quote Originally Posted by DrRocket
    Quote Originally Posted by dejawolf
    i tried to understand what the binomial coefficient is. and i brutally failed.

    http://www.mathwords.com/b/binomial_coefficients.htm

    this webpage which usually is pretty helpful.. well it confused me even further.
    Do you have a specific question?

    Here is a general explanation http://en.wikipedia.org/wiki/Binomial_coefficient
    and another http://mathworld.wolfram.com/BinomialCoefficient.html
    yeah, i've been throwing myself at both of those as well.
    so the binomial coefficient is basically the n and k inside the parentheses?
    when you have eliminated the impossible, whatever remains, however improbable, must be the truth
    A.C Doyle
    Reply With Quote  
     

  5. #4 Re: binomial coefficients 
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by dejawolf
    Quote Originally Posted by DrRocket
    Quote Originally Posted by dejawolf
    i tried to understand what the binomial coefficient is. and i brutally failed.

    http://www.mathwords.com/b/binomial_coefficients.htm

    this webpage which usually is pretty helpful.. well it confused me even further.
    Do you have a specific question?

    Here is a general explanation http://en.wikipedia.org/wiki/Binomial_coefficient
    and another http://mathworld.wolfram.com/BinomialCoefficient.html
    yeah, i've been throwing myself at both of those as well.
    so the binomial coefficient is basically the n and k inside the parentheses?
    I am not sure what to tell you beyond the first sentence in the Wiki article and the general expression in terms of factorials.

    What is it that is confusing you?
    Reply With Quote  
     

  6. #5 Re: binomial coefficients 
    Forum Professor sunshinewarrior's Avatar
    Join Date
    Sep 2007
    Location
    London
    Posts
    1,525
    Quote Originally Posted by dejawolf
    so the binomial coefficient is basically the n and k inside the parentheses?
    That is the way it is conventionally represented.

    What makes up these numbers?

    Well, the n is supposed to represent the total number of elements in whatever is under consideration (which is why they call it a set).

    It could, however, refer to a polynomial, or number of table settings, or the number of socks in a drawer. So this idea (the binomial coefficient) has a number of uses: whence its importance in maths and statistics.

    The k, therefore, is the number of items within n that you want to consider/test/check.

    When you put n and k together, as explained in the wiki article, you get a number, nCk, say, that represents your answer.

    Suppose your question was: If I take a handful (5) marbles out of a pot containing 20 distinct marbles, how many different types of handful are available?

    Here n is 20 (the number of distinct marbles

    and k is 5 (the number of marbles in a handful).

    By the formula given - n!/(k!(n-k)!)

    we get 15,504 distinct handfuls.

    There is another useful calculation that is complementary to Combination, and that is Permutation.

    In Permutation, the order in which the things are chosen is also relevant. Notice that in Combination (the binomial coefficient), it didn't matter in which order the 5 marbles landed in my hand. The only question was one of distinct handfuls.

    Suppose we considered, instead, 20 dinner guests and the way in which the first 5 are sat on the left of the hostess. Here, the order in which they appear is just as important as who is actually chosen. So the formula for the permutation (keeping with n and k, instead of the conventional n and r), is:

    n!/(n-k)!

    which gives 1,860,480.

    You can also calculate these binomial coefficient numbers in succession, by hand, using Pascal's Triangle, which also makes explicit why it is so useful in calculating the coefficients in binomial expansions (which is what made it possible for Newton to start inventing the calculus, for instance).

    I don't know if any of this exposition makes matters any clearer but, as DrRocket said, if you have a more specific query, please ask. After all, the wiki articles are quite well written, so there's not much more by way og general explanation that can be given.
    Reply With Quote  
     

Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •