You can put this solution on YOUR website!
Suppose that there is a large group of people, consisting of exactly 2N women and 2N men. The group is split in half at random. What is the probability that each half contains exactly N women and N men?
I don't like the answer I gave you.
Question: If the 4N people are split in half
how many split-pairs could there be.
We would have to have 2N in each half
How many ways can we get a group of 2N people
from a group of 4N people?
That should be (4N)C(2N) = (4N)!/[(4N-2N)!*(2N)!]
Only one of those sets has N women and N men.
The probability of there being N women and N men in
each of the halfs would be (1*2*...(2N))/[(4N)(4N-1)...(2N+1)]
As far as Stirling is concerned I don't know
anything about that.
Please post the problem again. Maybe someone else who
sees it can give you more help.