SOLUTION: 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 exac

Question 492769: 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?
And the second part asks for a given N, set up Stirling's Formula so you can calculate the approx value for a given N.
I am having trouble thinking how to set up this problem. I know as N gets bigger, the possible combinations increase....I'm thinking 2^n.
I also know that the order does not matter, but with each selection you are taking removing someone from the pool of 4N people.

Answer by stanbon(57969) (Show Source):
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?
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I don't like the answer I gave you.
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Question: If the 4N people are split in half
how many split-pairs could there be.
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We would have to have 2N in each half
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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)!]
= [(4N)(4N-1)...(2N+1)]/[1*2*...(2N)]
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Only one of those sets has N women and N men.
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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)]
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As far as Stirling is concerned I don't know
anything about that.
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Please post the problem again. Maybe someone else who
sees it can give you more help.
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Cheers,
Stan H.
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