6.6.36 Combinatorics

Problem: Find the coefficients for \( a=x^{3} \cdot y^{2} \cdot z^{2}, b=x^{2} \cdot y^{2} \cdot z^{2} \) and \( c=x^{4} \cdot z^{4} \) in the expansion \( \left(2 x+3 y+5 z^{2}\right)^{6} \).