Question 57
Find the value of
$$
\sum 17C_a \cdot 17C_b \cdot 17C_c,
$$
where the sum is taken over all triples $(a, b, c)$ of non-negative integers satisfying $a+b+c=5$.
$$
\sum 17C_a \cdot 17C_b \cdot 17C_c,
$$
where the sum is taken over all triples $(a, b, c)$ of non-negative integers satisfying $a+b+c=5$.