A class consists of 17 men and 14 women. An exam is given and students are ranked according to their performance. Assume no two students obtain the same score. If all rankings are considered equally likely, what is the probability that women receive the top 4 scores?
I know that there would be 31! total orderings, which would go in the denominator, but I can't think of how the numerator should look.
1) Any four women out of the 14 can occupy the top four ranks.
2) The can do so in any order among themselves.
3) Everyone else can occupy the other positions in any order.
Would it be something like (14 P 4)*(27!)/(31!)?