Question

The coefficient of $a^4{b}^3{c}^{2}d$ in the expansion of ${(a-b+c-d)}^{10}$ is

• A. ${(-1)}^4\frac{10!}{3!2!1!}$
• B. ${(-1)}^4\frac{10!}{2!1!}$
• C. ${(-1)}^4\frac{9!}{4!3!2!1!}$
• D. ${(-1)}^4\frac{10!}{4!3!2!1!}$

Answer 1

Answer: (D)

${(-1)}^4\frac{10!}{4!3!2!1!}$

The formula to find the coefficient of $a^p{b}^q{c}^r{d}^s$ in $(xa+yb+zc+vd{)}^n$ is $\frac{n!x^p{y}^q{z}^r{v}^s}{p!q!r!s!}$

So, coefficient of $a^4{b}^3{c}^{2}d$ in $(a-b+c-d{)}^{10}=\frac{10!1^4(-1{)}^3{1}^2(-1{)}^1}{4!3!2!1!}$=$\frac{10!(-1{)}^4}{4!3!2!1!}$