The total number of possible committees is C(8,4), because we're choosing 4 people from a group of 8, and order doesn't matter.
By parallel logic, the number of ways to choose 2 Democrats from 4 is C(4,2); and similarly for the Republicans. Thus the number of possible committees that meet our criteria is C(4,2)*C(4,2).
Then the probability of obtaining such a committee is [C(4,2)*C(4,2)]/C(8,4)
C(4,2) = 4!/(2!*2!) = 1*2*3*4/(1*2*1*2) = 12/2 = 6
By parallel logic, C(8,4) = (1*2*3*4*5*6*7*8)/(1*2*3*4*1*2*3*4) = (5*6*7*8) / (1*2*3*4) = 70
Thus, our fraction (and the answer) is (6*6)/70 = 36/70 = 18/35
