Of 100 patients with a certain disease, 10 were chosen at random to undergo a drug treatment that increases the cure rate from 50% for those not given the treatment to 75% for those given the drug treatment.

a. What is the probability that a randomly chosen patient both was cured and was given the drug treatment?

b. What is the probability that a patient who was cured had been given the drug treatment?

c. What is the probability that a specific group of 10 patients was chosen to undergo the drug treatment? (Leave your answer in terms of factorials.)