Question: 2015 Winter Final - 14
Let $S$ be a set of 100 integers; 30 of these are positive and the other 70 integers in $S$ are
negative. We choose, uniformly at random, a 20-element subset of $S$. What is the probability that
at least one of the elements in this subset is positive?
(a)
$1 - \left. {70 \choose 20} \middle/ {100 \choose 20} \right.$
(b)
$\left. {30 \choose 1} \middle/ {100 \choose 20} \right.$
(c)
$\left. {30 \choose 1}{70 \choose 19} \middle/ {100 \choose 20} \right.$
(d)
None of the above.