Question

Combinatorial Math:

Find the number of nonnegative integer solutions to the equation a+b+c=249. We are given:

10 ≤ a ≤ 30  (you can use an ellipsis between values in this factor instead of listing them all)

b is even and b > 50

c ≥ 144

a) Set up the generating function. Do not multiply it out. Do not use a, b or c in the function. Use x as the variable. The first factor should relate to a, the second to b and the third to c. (If a factor relates to an unending sum, list the first three terms and the ellipsis, e.g. (x+x^2+x^3+...).)

b) Explain what you would do to find the number of nonnegative integer solutions to the given equation.

Answer 1