Question: 2019 Winter Final - 3
Consider a set $S$ consisting of 25 beer bottles $b_1,b_2,...,b_{25}$ and 30 cider bottles $c_1,c_2,...,c_{30}$.
How many 10-element subsets of $S$ contain at least 2 beer bottles?
(a)
${55 \choose 10} - {30 \choose 10} - 25 \cdot {30 \choose 9}$
(b)
${55 \choose 10} - {30 \choose 10} - 25 \cdot {29 \choose 9}$
(c)
${55 \choose 10} - {30 \choose 10} - 25 \cdot {30 \choose 10}$
(d)
${55 \choose 10} - {30 \choose 10} - {30 \choose 9}$