Because of a mistake in packaging, a case of 12 bottles of red wine contained 5 Merlot and 7 Cabernet, each without labels. All the bottles look alike and have an equal probability of being chosen. Three bottles are randomly selected.
(a) What is the probability that all three are Merlot?
(b) What is the probability that exactly two are Merlot?
(c) What is the probability that none is a Merlot?