Question

${}^{10}{C}_1{+}^{10}{C}_3{+}^{10}{C}_5{+}^{10}{C}_7{+}^{10}{C}_9=$

• A. $2^9$
• B. $2^{10}$
• C. $2^{10}-1$
• D. $2^{10}+1$

Answer 1

The correct option is A $2^9$

We know that

$2^{n-1}={}^n{C}_0+{}^n{C}_2+{}^n{C}_4+...={}^n{C}_1+{}^n{C}_3+{}^n{C}_5+...$

So, ${}^{10}{C}_1+{}^{10}{C}_3+{}^{10}{C}_5+...+{}^{10}{C}_9=2^{10-1}=2^9$