This is how I solved it.
12 people are to be selected from 15, no. of ways = 15C12.
Now of these 15 people, 2/3 are men, so men = 2/3*15 = 10, hence women = 5.
Now we need to choose 12 people such that at least 2/3 of the 12 are men, that is 2/3*12= 8. So at least 8 should be men. So there can be maximum of 4 women. Now the max no. of women in our pool of 15 = 5. Therefore, if we can eliminate this particular case (when we choose all 5 women), then there are always at least 8 men.
Now when 5 women are chosen, no. of ways to choose the 12 people jury = 5C5*10C7. (since the other seven have to come from the remaining 10 men).
Therefore, the required probability is 1 - 5C5*10C7/(15C12) = 1 - 10*9*8/(15*14*13) = 1 - 24/91 = 67/91.
Hence D is the correct choice.
Let me know if this works
