Question 1198005
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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[24]^10}}} = {{{(24*23*22*21*20*19*18*17*16*15)/(1*2*3*4*5*6*7*8*9*10)}}} = 1961256.


The number of ways to select 5 men from 12 men is  {{{C[12]^5}}} = 792.

The number of ways to select 5 women from 12 women is the same  {{{C[12]^5}}} = 792.


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


The probability under the problem's question is

    P = {{{(C[12]^5*C[12]^5)/C[24]^10}}} = {{{(792*792)/1961256}}} = 0.319827702 = 0.3198  (rounded).    <U>ANSWER</U>
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Solved.