Car color preferences change over the years and according to the particular model that the customer selects. In a recent year, suppose that 10% of all luxury cars sold were black. If 25 cars of that year and type are randomly selected, find the following probabilities:
a. At least five cars are black.
b. At most six cars are black.
c. More than four cars are black.
d. Exactly four cars are black.
e. Between three and five cars (inclusive) are black.
f. More than 20 cars are not black.