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Pascal triangle

  1. Nov 6, 2003 #1

    MathematicalPhysicist

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    does pascal triangle use in this equation (a+b+c)^n i know it is used in (a+b)^n?

    and how could you solve for m number of numbers to the power n?
    (a+b+c+...+d)^n
    ||
    \/
    m numbers.
     
  2. jcsd
  3. Nov 6, 2003 #2

    HallsofIvy

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    No, Pascal's triangle give binomial coefficients.

    What you need are "multinomial" coefficients.

    The binomial coefficients are given by nCm= n!/(m!(n-m)!) because there are that many ways of arranging m x's and n-m y's to give the product xmyn-m.

    The "trinomial" coefficient for xiyjzk would be (i+j+k)!/(i! j! k!)

    If you have "m" numbers to the "n" power: (x1+ x2+...+xm)n then the "multi-nomial" coefficient for x1ixjj...xmk would be

    (i+ j+ ...+ k)!/(i! j! ... k!).
     
  4. Nov 8, 2003 #3

    MathematicalPhysicist

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    thanks :smile:
     
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