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Generating Function- change for a dollar

  1. Oct 5, 2009 #1
    1. The problem statement, all variables and given/known data

    If our currency consists of a two-cent coin and three kinds of pennies, how
    many ways can we make change for a dollar?

    2. Relevant equations

    3. The attempt at a solution

    the previous part to this problem led to this generating function:

    G(x)=(1+x)^3∑_(k≥0)▒〖((k+3)¦3)(〖x^2)〗^k 〗

    Am I supposed to put something in for x or for k? I don't know what to do. Any help would be great!!
  2. jcsd
  3. Oct 5, 2009 #2
    that is supposed to be the sum for all k greater than or equal to zero of [((k+3) choose 3)(x^2)^k]
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