Discrete Mathematics Level 4

For non-negative integers $$a,b,c$$ with their sum of 10, let the triplets $$(a_1,b_1,c_1), (a_2,b_2, c_2) , \ldots, (a_n, b_n, c_n)$$ denote the ordered triplets of $$(a,b,c)$$ such that $$\frac{10!}{a!b!c!}$$ is an integer.

Find the value of $$\displaystyle \sum_{j=1}^n \frac{10!}{(a_j)!(b_j)!(c_j)!}$$.

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