Generating function?

Computer Science Level pending

Let \(a,b,c\) and \(d\) be non-negative integers satisfying \(a+b+c+d=360 \), and that \(b,c,d\) are multiplies of 2, 3, 5, respectively.

Let \(P \) denote the total number of solutions satisfying the condition above, and
\(Q\) denote the total number of solutions satisfying the condition above with an additional constraint of \(a= 0 \).

Find the sum of the first 7 digits of \(\dfrac QP \) after the decimal point.


I did label this question as computer science because I did it that way. If anyone know how to solve it with generating function, please help.
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