Five construction companies each offer bids on three distinct Department of Transportation (DOT) contracts. A particular company will be awarded at most one DOT contract.
a. How many different ways can the bids be awarded?
b. Under the assumption that the simple events are equally likely, find the probability that company 2 is awarded a DOT contract.
c. Suppose that companies 4 and 5 have submitted noncompetitive bids. If the contracts are awarded at random by the DOT, find the probability that both these companies receive contracts.