Question

The coefficient of the $8$th term in the expansion of $(1+x{)}^{10}$ is

• A. $120$
• B. $7$
• C. ${}^{10}{C}_8$
• D. $210$

Answer 1

The correct option is A $120$

$(1+x{)}^{10}=$ ${}^{10}{C}_0+{}^{10}{C}_{1}x+{}^{10}{C}_2{x}^2+........+{}^{10}{C}_7{x}^7+{}^{10}{C}_8{x}^8+{}^{10}{C}_9{x}^9+{}^{10}{C}_{10}{x}^{10}$

So here, first term is ${}^{10}{C}_0$ then $8^{th}$ term will be $10C_7{x}^7.$

$\Rightarrow$ Coefficient of the $8^{th}$ term $={}^{10}{C}_7$

$=\frac{10!}{7!3!}$

$=\frac{10\times 9\times 8\times 7!}{7!\times 3\times 2\times 1}$

$=120$