A task force established by the Environmental Protection Agency was scheduled to investigate 20 industrial firms to check for violations of pollution control regulations. However, budget cutbacks have drastically reduced the size of the task force, and they will be able to investigate only 3 of the 20 firms. If it is known that 5 of the firms are actually operating in violation of regulations, find the probability that
a. None of the three sampled firms will be found in violation of regulations.
b. All three firms investigated will be found in violation of regulations.
c. At least 1 of the 3 firms will be operating in violation of pollution control regulations.