6.6.64 Combinatorics

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