Question

The value of $\sum _{0⩽i<8}\sum _{i<j⩽8}j{.}^8{\text{C}}_i$ is

• A. $3200$
• B. $6200$
• C. $6400$
• D. None of these

Answer 1

Answer: (C)

$6400$

${\sum }_{0\le i<j\le 8}{\sum }_{i<j\le 8}j{.}^8{\text{C}}_i\left[\right(i+1)+(i+2)+......(i+8\left)\right]$
$={\sum }_{0\le i<j\le 8}{\text{C}}_i\left[\right(1+2+....+8)-(1+2+.....+i\left)\right]$
$={\sum }_{0\le i<8}{\text{C}}_i(36-\frac{i(i+1)}{2})=6400$