Question

The value of ${}^{10}{C}_1{+}^{10}{C}_2{+}^{10}{C}_3+....{+}^{10}{C}_9$ is

• A. $2^{10}$
• B. $2^{11}$
• C. $2^{10}-2$
• D. $2^{10}-1$

Answer 1

Answer: (C)

Since, ${\left(1+x\right)}^n{=}^n{C}_0{+}^n{C}_{1}x{+}^n{C}_2{x}^2+...{+}^n{C}_n{x}^n$
Put x = 1 and n = 10, we get
$2^{10}{=}^{10}{C}_0{+}^{10}{C}_1{+}^{10}{C}_2+...{+}^{10}{C}_{10}$
$2^{10}=1{+}^{10}{C}_1{+}^{10}{C}_2+...{+}^{10}{C}_9+1$
$2^{10}-2{=}^{10}{C}_1{+}^{10}{C}_2+...{+}^{10}{C}_9$