Question

The value of ${}^{10}{C}_1+{}^{10}{C}_3+{}^{10}{C}_5+{}^{10}{C}_7+{}^{10}{C}_9$ is

• A. $2^7$
• B. $2^8$
• C. $2^9$
• D. $2^{10}$

Answer 1

The correct option is C $2^9$

We know that
${}^n{C}_1+{}^n{C}_3+{}^n{C}_5+\dots =2^{n-1}$
So,
${}^{10}{C}_1+{}^{10}{C}_3+{}^{10}{C}_5+{}^{10}{C}_7+{}^{10}{C}_9=2^{10-1}=2^9$