Question 1160047
What is the probability that there will be NO man.
This means that both are women
The denominator is choosing 2 from 30 or 30C2=435
the numerator is 18C0, which =1, times 12C2=66
the answer 1-(66/435) or 369/435=0.8483

Do this more simply by recognizing the probability of the first being a woman is 12/30 and the second is 11/29
for a product of 132/870 or 0.1517.  Everything else is at least one man or 1-0.1517 or 0.8483

Can check this crudely. 
40% are women or 2/5. The likelihood of both women is approximately (2/5)^2=4/25=0.16
Otherwise, they are men, and 1-0.16=0.84, close to what was obtained.