Question: 2015 Fall Final - 1

Author: Michiel Smid

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)

(\binom{15}{3}) + (\binom{15}{2}) \cdot 5 + 15 \cdot (\binom{5}{2})

(b)

(\binom{15}{3})

(c)

(\binom{20}{3})

(d)

(\binom{15}{3}) + 15 \cdot (\binom{5}{2})