Question

The value of
$({{}^{7}C}_0+{{}^{7}C}_1)+({{}^{7}C}_1+{{}^{7}C}_2)+.....({{}^{7}C}_6+{{}^{7}C}_7)$ is

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

Answer 1

The correct option is B $2^8-2$

${(}^7{C}_0{+}^7{C}_1+..{.}^7{C}_6)+{(}^7{C}_1{+}^7{C}_2+..{.}^7{C}_7)$

$\left(2^7{-}^7{C}_7\right)+\left(2^7{-}^7{C}_0\right)$

$(2^7-1)+(2^7-1)$

${2.2}^7-2$

$2^8-2$