Question

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

• A. $10!$
• B. $2520$
• C. $\frac{10!}{8!4!9!9!}$
• D. $\frac{10!}{7!3!8!8!}$

Answer 1

The correct option is B $2520$

$(abcd{)}^{10}{[\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}]}^{10}$
$\therefore$ Required co-efficient $=a^{-2}{b}^{-6}{c}^{-1}{d}^{-1}$ in
${(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d})}^{10}$
$=\frac{10!}{2!6!1!1!}=2520$ (Number of ways to form the group of 6,2,1 and 1 from 10 objects)