6.6.13 Combinatorics

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