Q. The coefficient of $a^{3}b^{4}c$ in the expansion of ${(1 + a - b + c)}^{9}$is equal to
A) $\frac{9!}{3!6!}$
B) $\frac{9!}{4!5!}$
C) $\frac{9!}{3!5!}$
D) $\frac{9!}{3!4!}$
Explanation
(d)
$(1 + a - b + c)^{9} = \sum_{}^{}{\frac{9!}{x_{1}!x_{2}!x_{3}!x_{4}!} \bullet (1)^{x_{1}}(a)^{x_{2}}( - b)^{x_{3}}(c)^{x_{4}}}$
$\Longrightarrow Coefficient\ of\ a^{3}b^{4}c = \frac{9!}{1!3!4!1!} = \frac{9!}{3!4!}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.