Question: 2015 Fall Midterm - 2
Let $S$ be a set of 25 elements and let $x$, $y$, and $z$ be three distinct elements of $S$. What is
the number of subsets of $S$ that contain both $x$ and $y$, but do not contain $z$?
(a)
$2^{23}$
(b)
$2^{25} - 2^{24} + 2^{23}$
(c)
$2^{22}$
(d)
$2^{25} - 2^{22}$