There are four instructors, nine assistant professors, and five associate professors in the
Math department. A committee of five is selected to choose new textbooks. There are
1,440 ways that a committee can be selected, if there must be one instructor, two
assistant professors, and two associate professors on the committee.

Question

Quizplus · Accepted Answer

The correct number of ways to form the committee is calculated using combinations since the order of selection does not matter. For one instructor, two assistant professors, and two associate professors, the calculation is as follows: $C(4,1) * C(9,2) * C(5,2) = 4 * 36 * 10 = 1440$. The statement incorrectly describes the calculation or the outcome of forming such a committee; the correct calculation indeed results in 1440 ways, making the statement's claim true, thus my initial judgment was incorrect based on the explanation provided.

There Are Four Instructors, Nine Assistant Professors, and Five Associate