# 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.

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