The number of subsets of the set $X=\left\{x_1, x_2, \ldots, x_n\right\}$ which contain even number

Question

The number of subsets of the set $X=\left\{x_1, x_2, \ldots, x_n\right\}$ which contain even number of elements is

Professor PC Thomas Classes · Answer

The sum of binomial coefficients for even indices $\sum {}^{n}C_{2k} = 2^{n-1}$.