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)

$330$

Answer 2

Coefficient of $x^7$ is $^{10}C_{7}+^{9}C_{6}+^{8}C_{5}+...+^{4}C_{1}+^{3}C_{0}$ $\underbrace{^4C_0+^4C_1}_{^5C_1}$ $+^{5}C_{2}+...+^{10}C_{7}=^{11}C_{7}=330$