Q. The value of $\left( {\ ^{7}C}_{0} + {\ ^{7}C}_{1} \right) + \left( {\ ^{7}C}_{1} + {\ ^{7}C}_{2} \right) + \ldots + \left( {\ ^{7}C}_{6} + {\ ^{7}C}_{7} \right)is$
A) $2^{8} - 1$
B) $2^{8} + 1$
C) $2^{8}$
D) $2^{8} - 2$
Explanation
(d)
$\left( \ ^{7}C_{0} + \ ^{7}C_{1} \right) + \left( \ ^{7}C_{1} + \ ^{7}C_{2} \right) + \ldots + \left( \ ^{7}C_{6} + \ ^{7}C_{7} \right)$
$= \ ^{8}C_{1} + \ ^{8}C_{2} + \ldots + \ ^{8}C_{7} + \left( \ ^{8}C_{0} + \ ^{8}C_{8} \right) - \left( \ ^{8}C_{0} + \ ^{8}C_{8} \right)$
$= 2^{8} - 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.