Question
The coefficient of $$a^3 b^4 c$$ in the expansion of $${\left( {1 + a - b + c} \right)^9}$$ is equal to
A.
$$\frac{{9!}}{{3!6!}}$$
B.
$$\frac{{9!}}{{4!5!}}$$
C.
$$\frac{{9!}}{{3!5!}}$$
D.
$$\frac{{9!}}{{3!4!}}$$
Answer :
$$\frac{{9!}}{{3!4!}}$$
Solution :
$$\eqalign{
& {\left( {1 + a - b + c} \right)^9} \cr
& = \sum {\frac{{9!}}{{{x_1}!{x_2}!{x_3}!{x_4}!}} \cdot {{\left( 1 \right)}^{{x_1}}}{{\left( a \right)}^{{x_2}}}{{\left( { - b} \right)}^{{x_3}}}{{\left( c \right)}^{{x_4}}}} \cr} $$
$$ \Rightarrow $$ Coefficient of $${a^3}{b^4}c = \frac{{9!}}{{1!3!4!1!}} = \frac{{9!}}{{3!4!}}$$