Question: 2019 Fall Midterm - 7
What does
$$
{w \choose 3} \cdot {m \choose 2} + {w \choose 4} \cdot m + {w \choose 5}
$$
count?
(a)
The number of ways to choose 5 people out of a group consisting of $w$ women and $m$ men,
where at most 3 men can be chosen.
(b)
The number of ways to choose 5 people out of a group consisting of $w$ women and $m$ men,
where at most 3 women can be chosen.
(c)
The number of ways to choose 5 people out of a group consisting of $w$ women and $m$ men,
where at least 3 men must be chosen.
(d)
The number of ways to choose 5 people out of a group consisting of $w$ women and $m$ men,
where at least 3 women must be chosen.