# Math Help - Generating Function Application Question

1. ## Generating Function Application Question

Alan and Bob have stolen a total of $10,000 from the bank, in the form of fifty$20 bills, forty $50 bills, and seventy$100 bills. How many ways are there to split the loot evenly between them? Express your answer as a coefficient of a generating function.

I'm having trouble solving this cause I am not sure how to fit all the conditions into a generating function.

Any tips?

Thanks

2. The coefficient of $x^{5000}y^{5000}$ in the expression:

$
(\sum_{i=0}^{50}(x^{20})^i(y^{20})^{50-i})
(\sum_{i=0}^{40}(x^{50})^i(y^{50})^{40-i})
(\sum_{i=0}^{70}(x^{100})^i(y^{100})^{70-i})
$

Power of x represents money given to Alan, and power of y represents money given to Bob.
I think you can see how all the numbers fit together.

Definitely wouldn't want to calculate this by hand