Results 1 to 3 of 3

Math Help - pascal terms

  1. #1
    Senior Member furor celtica's Avatar
    Joined
    May 2009
    Posts
    271

    pascal terms

    ok so i'm using the notation (n r) for a pascal term

    state numbers a, b and c such that
    a*(8 5)=b*(8 6)=c*(7 5)

    i thought this should be easy: i made three separate equation and developed the pascal terms into factorials like (8 5) = 8!/5!*3! = 8x7x6/2x3 but i just end up with stuff i don't know how to develop. how would you do this? i think there's just something simple im missing
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,596
    Thanks
    1421
    I think that, by "Pascal term", you mean what I would call a "binomial coefficient; the numbers in Pascal's triangle, \begin{pmatrix}n \\ m \end{pmatrix}= \frac{n!}{m!(n- m)!}

    Yes, \begin{pmatrix}8 \\ 5\end{pmatrix}= \frac{8(7)(6)}{3(2)}= 42
    \begin{pmatrix}8 \\ 6\end{pmatrix}= \frac{8(7)}{2}= 14 and
    \begin{pmatrix}7 \\ 5\end{pmatrix}= \frac{7(6)}{1}= 42

    so your equation is 42a= 14b= 42c. That is two independent equations (42a= 14b and 42a= 42c; they imply 42a= 42c but this is not independent.) Those reduce to 3a= b and a= c. Unless you have additional information you have not told us there are an infinite collection of solutions. Choose any number for a. Then b= 3a and c= a. For example, if you arbitrarily choose a= 3, b= 9 and c= 3 satisfy the equations. If you choose a= 4.3, b= 12.9 and c= 4.3 also satisfy the equations.
    Last edited by HallsofIvy; October 12th 2010 at 03:51 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member furor celtica's Avatar
    Joined
    May 2009
    Posts
    271
    i think you got (7 5) wrong, its 42
    this is all the info i have
    i have the answers and they are a, b, c are all different, i.e. not equal to one another, and they are specific, no infinite collection
    but i'd like to know how to get them, i don't care for plain answers
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Pascal
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 28th 2009, 05:19 PM
  2. Pascal's Triangle
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 1st 2008, 11:02 AM
  3. Pascal's Triangle
    Posted in the Discrete Math Forum
    Replies: 10
    Last Post: May 31st 2007, 07:12 AM
  4. Pascal's theorem
    Posted in the Algebra Forum
    Replies: 7
    Last Post: March 23rd 2007, 11:42 PM
  5. Pascal's Trianglw
    Posted in the Statistics Forum
    Replies: 4
    Last Post: December 11th 2006, 08:52 PM

Search Tags


/mathhelpforum @mathhelpforum