SOLUTION: Ten-member jury for a criminal case will be selected from a pool of 12 men and 12 women. What is the probability that the jury will have 5 men and 5 women?

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Question 1198005: Ten-member jury for a criminal case will be selected from a pool of 12 men and 12 women. What is the
probability that the jury will have 5 men and 5 women?

Answer by ikleyn(52777) About Me  (Show Source):
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Ten-member jury for a criminal case will be selected from a pool of 12 men and 12 women.
What is the probability that the jury will have 5 men and 5 women?
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The total number of different ways to select ten-member jury from 12+12 = 24 persons (candidates) is

    C%5B24%5D%5E10 =  = 1961256.


The number of ways to select 5 men from 12 men is  C%5B12%5D%5E5 = 792.

The number of ways to select 5 women from 12 women is the same  C%5B12%5D%5E5 = 792.


The number of different possible 5men-5women juries is the product  792*792.


The probability under the problem's question is

    P = %28C%5B12%5D%5E5%2AC%5B12%5D%5E5%29%2FC%5B24%5D%5E10 = %28792%2A792%29%2F1961256 = 0.319827702 = 0.3198  (rounded).    ANSWER

Solved.