Question

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?

Answer 1

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:

`C(7, 4) = (7!)/(4!(7 - 4)!)`

`= (5040)/(4!3!)`

`= (5040)/(24 \cdot 6)`

`= (5040)/(144) = 35`

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


`\text{P(4 women): } (35)/(495) = (7)/(99)`