Question

${}^{15}{C}_3+{}^{15}{C}_5+.....+{}^{15}{C}_{15}$ will be equal to

• A. $2^{14}$
• B. $2^{14}-15$
• C. $2^{14}+15$
• D. $2^{14}-1$

Answer 1

Answer: (B)

We know,
${}^{15}{C}_1+{}^{15}{C}_3+{}^{15}{C}_5+\dots +{}^{15}{C}_{15}=2^{15-1}$
$\therefore {}^{15}{C}_3+{}^{15}{C}_5+\dots +{}^{15}{C}_{15}=2^{14}-15$