Question: 2015 Fall Final - 1
Consider a set $S$ consisting of 20 integers; 5 of these are strictly positive and the other 15
integers in $S$ are strictly negative. What is the number of 3-element subsets of $S$ having the
property that the product of the 3 elements in the subset is negative?
(a)
${20 \choose 3}$
(b)
${15 \choose 3} + {15 \choose 2} \cdot 5 + 15 \cdot {5 \choose 2}$
(c)
${15 \choose 3}$
(d)
${15 \choose 3} + 15 \cdot {5 \choose 2}$