Question

${}^{15}{C}_3{+}^{15}{C}_5+.......{+}^{15}{C}_{15}=$

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

Answer 1

Answer: (B)

${}^{15}{C}_3+{}^{15}{C}_5+............+{}^{15}{C}_{15}$
$=\left({}^{15}{C}_1+{}^{15}{C}_3+{}^{15}{C}_5+.....+{}^{15}{C}_{15}\right)-{}^{15}{C}_1$
$=\frac{2^{15}}{2}-15$
$=2^{14}-15$