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(75887)   (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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