Question

A college math department consisting of 10 faculty members must choose a department head, an assistant department head, and a faculty senate representative. In how many ways can this be done?

Answer 1

The number of ways to choose a department head, assistant department head, and faculty senate representative from 10 faculty members is 720 ways.

Step-by-step explanation:

To solve the problem of how many ways a college math department of 10 faculty members can choose a department head, an assistant department head, and a faculty senate representative, we treat this as a permutation problem since the order of selection matters and individuals cannot fulfill more than one role at the same time.

First, we select the department head. There are 10 possible choices. After choosing the department head, we are left with 9 candidates for the assistant department head.

Finally, we have 8 remaining candidates for the faculty senate representative role. The formula for permutations (without repetition) is the product of the available choices at each stage.

Therefore, the total number of ways to choose the three positions is:

10 (for the department head) × 9 (for the assistant department head) × 8 (for the senate representative) = 720 ways.