Question: 2017 Winter Final - 3
Let $B$ be a set consisting of 45 bottles. Out of these, 17 are beer bottles, and the remaining 28
are cider bottles. Consider subsets of $B$ that contain
- exactly 5 beer bottles and zero or more cider bottles,
- exactly 5 cider bottles and zero or more beer bottles.
(a)
$ 2^{45} - {17 \choose 5} - {28 \choose 5} $
(b)
$ {17 \choose 5} \cdot 2^{28} + 2^{17} \cdot {28 \choose 5} - {17 \choose 5} \cdot {28 \choose 5} $
(c)
$ 2^{45} - {17 \choose 5} \cdot {28 \choose 5} $
(d)
$ {17 \choose 5} \cdot 2^{28} + 2^{17} \cdot {28 \choose 5} $