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Mathematics
15C3 + 15C5 + .. ...+ 15C15 will be equal to
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Q. $^{15}C_{3} +\,{}^{15}C_{5} + .. ...+\,{}^{15}C_{15} $ will be equal to
WBJEE
WBJEE 2011
Permutations and Combinations
A
$2^{14}$
0%
B
$2^{14} - 15$
0%
C
$2^{14} + 15$
0%
D
$2^{14} - 1$
100%
Solution:
We know,
${ }^{15} C_{1}+{ }^{15} C_{3}+{ }^{15} C_{5}+\ldots+{ }^{15} C_{15}=2^{15-1}$
$\therefore { }^{15} C_{3}+{ }^{15} C_{5}+\ldots+{ }^{15} C_{15}=2^{14}-15$