Question

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

• A. $10!$
• B. $\frac{10!}{8!4!9!9!}$
• C. $2520$
• D. None of these

Answer 1

The correct option is C $2520$

$(abc+bcd+abd+acd{)}^{10}$ can be written as $\left(abcd{)}^{10}\right(a^{-1}+b^{-1}+c^{-1}+d^{-1}{)}^{10}$

Using binomial theorem, the coefficient of $a^8{b}^4{c}^9{d}^9$ will be the coefficient of the powers $2,6,1,1$, that is

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