Question

$\left({}^7{C}_0{+}^7{C}_1\right)+\left({}^7{C}_2{+}^7{C}_3\right)+....+\left({}^7{C}_6{+}^7{C}_7\right)=$

• A. $2^8-2$
• B. $2^7-1$
• C. $2^7$
• D. $2^8-1$
• E. $2^7-2$

Answer 1

Answer: (C)

$\left({}^7{C}_0+{}^7{C}_1\right)+\left({}^7{C}_2+{}^7{C}_3\right)+...+\left({}^7{C}_6+{}^7{C}_7\right)$
$={}^7{C}_0+{}^7{C}_1+\dots +{}^7{C}_7$
$=2^7\left[\because C_0+C_1+C_2+...+C_n=2^n\right]$