Question

Passage:
If n is a positive and $a_1,a_2,a_3,..a_m\in C$ then
$(a_1+a_2+a_3+....+a_m{)}^n=\Sigma \left(\frac{n!}{n_1!n_2!n_3!\dots n_m!}\right)a_1^{n_1}{a}_2^{n_2}{a}_3^{n_3}....a_m^{n_m}$
where $n_1,n_2,n_3,n_m$ are all non negative integers subject to the condition
$n_1+n_2+n_3+\dots +n_m=n$
The coefficient of $x^3{y}^{4}z$ in the expansion of $(1+x-y+z{)}^9$ is

• A. $2320$
• B. $2420$
• C. $2520$
• D. $2620$

Answer 1

Answer: (C)

$2520$

The coefficient of $x^3{y}^{4}z$ will be $\frac{9!}{3!4!1!(9-(4+3+1\left)\right)!}$.

$=\frac{9!}{3!4!1!1!}$

$=\frac{\mathrm{9.8.7.6.5}}{3!}$

$=\mathrm{9.8.7.5}$
$=\mathrm{40.9.7}$
$=360.7$
$=2520$