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:
[tex]C(7, 4) = \frac{7!}{4!(7 - 4)!}[/tex]
[tex]= \frac{5040}{4!3!}[/tex]
[tex]= \frac{5040}{24 \cdot 6}[/tex]
[tex]= \frac{5040}{144} = 35[/tex]
Now, the total number of arrangements, without restriction, is simply: C(12, 4) because we don't care who we pick.
[tex]\text{P(4 women): } \frac{35}{495} = \frac{7}{99}[/tex]
