The results of the rigorous examination of a dozen automobile tires showed the following: one tire was perfect, three had only slight flaws in appearance, two had incompletely formed treads, one had a...

The results of the rigorous examination of a dozen automobile tires showed the following: one tire was perfect, three had only slight flaws in appearance, two had incompletely formed treads, one had a serious structural defect, and the rest had at least two of these defects. What is the probability that the next set of four tires you buy of this particular brand:

(a) Will be perfect?

(b) Will have at most only undesirable appearances?

(c) Will have fewer than two defects?