Question

$\frac{{}^{15}{C}_1}{{}^{15}{C}_0}+2.\frac{{}^{15}{C}_2}{{}^{15}{C}_1}+3.\frac{{}^{15}{C}_3}{{}^{15}{C}_2}+\dots +15.\frac{{}^{15}{C}_{15}}{{}^{15}{C}_{14}}=$

• A. 105
• B. 91
• C. 120
• D. 15

Answer 1

The correct option is C 120

As in the hint , This is the first step. Now we have to find sum of $r(n-r+1)/r$ = sum of $(n-r+1)$ =
$n\ast n-n(n+1)/2+n=n(n+1)/2$. Here n= 15 which gives answer 120.