Question

The coefficient of $a^8{b}^4{c}^9{d}^9$ in $(abc+abd+acd+bcd{)}^{10}$ is

Answer 1

Coefficient of $a^8{b}^4{c}^9{d}^9$

${(abc+abd+acd+bcd)}^{10}$

$={\left(abcd\right)}^{10}{(a^{-1}+b^{-1}+c^{-1}+d^{-1})}^{10}$

$\therefore$ Coeff. of $a^8{b}^4{c}^9{d}^9=$ Coeff of $a^2{b}^6{c}^1{d}^1$ in ${(a^{-1}+b^{-1}+c^{-1}+d^{-1})}^{10}$

$=\frac{10!}{2!6!1!1!}=2520$