15. Let $X=\{1,2,3, \ldots, 17\}$. Find the number of subsets $Y$ of $X$ with odd cardinalities.
15. Ans: 65536

The answer is
$$
\binom{17}{1}+\binom{17}{3}+\binom{17}{5}+\cdots+\binom{17}{17}=2^{16}=65536
$$