Suppose 5 men and 7 women are on a crowded elevator. at the next floor, four people get off the elevator. find the probability that all are women?

The total number of arrangements for all of them to be women is:
C(7, 4) because the order does not matter; we'd still have the same arrangements.

Now, we can simplify this:





Now, the total number of arrangements, without restriction, is simply: C(12, 4) because we don't care who we pick.