1 .
Let $m \geq 2$ and $n \geq 2$ be integers. What does
$$
{m \choose 2} + {n \choose 2} + mn
$$
count?
(a)
The number of ways to choose an unordered pair of people from a group consisting of $m$ men and $n$ women, where at least one man must be chosen.
(b)
The number of ways to choose an unordered pair of people from a group consisting of $m$ men and $n$ women.
(c)
The number of ways to choose an ordered pair $(x,y)$ from a group consisting of $m$ men and $n$ women, where $x$ must be a man and $y$ must be a woman.
(d)
The number of ways to choose an ordered pair $(x,y)$ from a group consisting of $m$ men and $n$ women, where $x$ and $y$ cannot both be men.