Question: 2019 Fall Final - 5
You are given 20 beer bottles $B_1,B_2,...,B_{20}$ and 50 cider bottles $C_1,C_2,...,C_{50}$.
Consider subsets of these 70 bottles, that contain at least 3 beer bottles (and any number of cider bottles). How many such subsets are there?
Consider subsets of these 70 bottles, that contain at least 3 beer bottles (and any number of cider bottles). How many such subsets are there?
(a)
$2^{70} - 2^{50} - 20 \cdot 2^{50}$
(b)
$2^{70} - 2^{50} - 20 - {20 \choose 2}$
(c)
$2^{70} - 2^{50} - 20 \cdot 2^{50} - {20 \choose 2} \cdot 2^{50}$
(d)
None of the above.