Question: 2015 Fall Final - 2
Consider a set $S$ consisting of 20 integers. The integer 0 is an element of $S$, 9 elements in $S$
are strictly positive, and the remaining 10 elements are strictly negative. What is the number of
7-element subsets of $S$ having the property that the product of the 7 elements in the subset is
equal to 0?
(a)
${20 \choose 6}$
(b)
${19 \choose 6}$
(c)
${20}\choose{7}$
(d)
${19 \choose 7}$