Question

The coefficient of $x^3{y}^{4}z$ in the expansion of $(1+x+y-z{)}^9$ is

• A. $2{.}^9{C}_7{.}^7{C}_4$
• B. $-2{.}^9{C}_2{.}^7{C}_3$
• C. ${}^9{C}_7{.}^7{C}_4$
• D. None of these

Answer 1

Answer: (B)

$-2{.}^9{C}_2{.}^7{C}_3$

$\begin{array}{c}{\left(1+x+y-z\right)}^9=\frac{|!9}{|!\alpha |!\beta |!\gamma |!\delta }{\left(x\right)}^{\alpha }{\left(y\right)}^{\beta }{\left(-z\right)}^{\delta }{\left(1\right)}^{\gamma }\\ where\alpha +\beta +\delta +\gamma =9\\ \alpha =3\\ \beta =4\\ \delta =1\\ \gamma =1\\ Coefficientof{x}^2{y}^{2}zis:-\frac{|!9}{|!3|!4}\\ -\frac{|!9}{|!2|!7}\times |!2\frac{|!7}{|!3|!4}\\ =-2\times {}^9{C}_7\times {}^7{C}_3\\ =-2\times {}^9{C}_7\times {}^7{C}_3\\ Hence,\\ optionBiscorrectanswer.\end{array}$