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)

$2^{14} - 15$

Answer 2

We know,
${ }^{15} C_{1}+{ }^{15} C_{3}+{ }^{15} C_{5}+\ldots+{ }^{15} C_{15}=2^{15-1}$
$\therefore{ }^{15} C_{3}+{ }^{15} C_{5}+\ldots+{ }^{15} C_{15}=2^{14}-15$