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

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 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? ---- 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)!] = [(4N)(4N-1)...(2N+1)]/[1*2*...(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. ==================================== Cheers, Stan H. ==============