An oil exploration firm has enough capital to finance 10 explorations. Suppose that the probability of striking oil on each exploration is 0.2 and the explorations are independent. The firm conducts the 10 explorations.

(a) Calculate the probability that the firm strikes oil on exactly 3 explorations.

(b) Calculate the probability that the firm does not strike oil on any of the explorations.

(c) If each successful exploration (i.e one that strikes oil) costs $50,000 and each unsuccessful exploration costs $20,000, calculate the expected total cost of the 10 explorations.