Question: 2017 Fall Final - 5
Let $n \geq 3$ and $m \geq 3$ be integers. What does
$$
{n \choose 3} + {m \choose 3} + n \cdot {m \choose 2} + m \cdot {n \choose 2}
$$
count?
(a)
The number of subsets having size 3 of a set consisting of $n$ positive numbers and $m$ negative numbers.
(b)
The number of subsets having size 2 or 3 of a set consisting of $n$ positive numbers and $m$ negative numbers.
(c)
The number of subsets having size 2 and 3 of a set consisting of $n$ positive numbers and $m$ negative numbers.
(d)
The number of subsets having size at most 3 of a set consisting of $n$ positive numbers and $m$ negative numbers.