There are four instructors nine assistant professors and fiv

There are four instructors, nine assistant professors, and five associate professors in the Math department. A committee of five is selected to plan the department corn roast. How many ways can a committee be selected, if there must be one instructor, two assistant professors, and two associate professors on the committee.

Solution

There are 4C1 = 4 ways to choose one instructor.

There are 9C2 = 36 ways to choose 2 asst profs.

There are 5C2 = 10 ways to choose 2 assoc profs.

Thus, that\'s a total of 4*36*10 = 1440 ways [ANSWER]