Question

The coefficient of $x^7$ in the expression ${\left(1+x\right)}^{10}+x{\left(1+x\right)}^9+x^2{\left(1+x\right)}^8+...+x^{10}$ is :

• A. $420$
• B. $330$
• C. $210$
• D. $120$

Answer 1

Answer: (B)

Coefficient of $x^7$ is
${}^{10}{C}_7{+}^9{C}_6{+}^8{C}_5+...{+}^4{C}_1{+}^3{C}_0$
$\underset{{}^5{C}_1}{\underbrace{{}^4{C}_0{+}^4{C}_1}}$${+}^5{C}_2+...{+}^{10}{C}_7{=}^{11}{C}_7=330$