Question

Solve this combination​

Answer 1

Consider the Binomial Expansion:

$(1 + x)^{15}= {15 \choose{0} }+ x \binom{15}{1} + ... + {x}^{15} \binom{15}{15}$

Substituting x = 1

$\binom{15}{0} + \binom{15}{2} + ... + \binom{15}{15} = {2}^{15}$

$\binom{15}{1} + \binom{15}{2} + ... + \binom{15}{15} = {2}^{15} - 1$

$\boxed{ \sf¹⁵C _{1} + ¹⁵C_{2} + ... + ¹⁵C_{15} = {2}^{15} - 1}$