Question: 2019 Winter Final - 5
Let $m \geq 2$ and $n \geq 2$ be integers. Why does the identity
$$
{m + n \choose 2} = {m \choose 2} + {n \choose 2} + mn
$$
hold?
(a)
None of the above.
(b)
Because both sides count the number of ordered pairs in a set of size $m + n$.
(c)
Because both sides count the number of ways $m$ men and $n$ women can be arranged on a line,
such that no two men are standing next to each other.
(d)
Because both sides count the number of 2-element subsets of a set of size $m + n$.