1. A security service employing 10 officers has been asked to provide 3 persons for crowd control at a local carnival. In how many different ways can the firm staff this event?
2. A corporate board of directors consisting of 15 persons is to form a subcommittee of 5 persons to examine an environmental issue currently facing the firm. How many different subcommittees are possible?
3. The chairperson of the accounting department has three summer courses available: Accounting 201, Accounting 202, and Accounting 305. Twelve faculty members are available for assignment to these courses, and no faculty member can be assigned to more than one course. In how many ways can the chairperson assign faculty to these courses?
4. A test to compare the taste of 6 soft drinks is being arranged. Each participant will be given 3 of the soft drinks and asked to indicate which one tastes best.
a. How many different possibilities exist for the set of soft drinks that a given participant will taste?
b. If we consider the order in which the participant in part (a) tastes the 3 soft drinks, how many possibilities exist?