Nausea and vomiting after surgery are common side effects of anesthesia and painkillers. Six different drugs, varying in cost, were compared for their effectiveness in preventing nausea and vomiting (New England Journal of Medicine, June 10, 2004). The medical researchers looked at all possible combinations of the drugs as treatments, including a single drug, as well as two-drug, three-drug, four-drug, five-drug, and six-drug combinations.

a. How many two-drug combinations of the six drugs are possible?

b. How many three-drug combinations of the six drugs are possible?

c. How many four-drug combinations of the six drugs are possible?

d. How many five-drug combinations of the six drugs are possible?

e. The researchers stated that a total of 64 drug combinations were tested as treatments for nausea. Verify that there are 64 ways that the six drugs can be combined. (Remember to include the one-drug and six-drug combinations as well as the control treatment of no drugs.)