Question: 2018 Winter Final - 1
You are given 20 beer bottles $B_1,B_2,\dots,B_{20}$ and 50 cider bottles $C_1,C_2,\dots,C_{50}$.
Consider subsets of these 70 bottles, consisting of 30 bottles, exactly 12 of which are beer
bottles. How many subsets are there?
(a)
${20 \choose 12} \cdot {38 \choose 18}$
(b)
${20 \choose 12} \cdot {50 \choose 18}$
(c)
${70 \choose 30} \cdot {20 \choose 12}$
(d)
${50 \choose 12} \cdot {20 \choose 18}$