An athletics department staff member is permitted to promote which of the following?

The correct answer is that an athletics department staff member is not permitted to promote any of the listed options. NCAA rules govern and restrict the activities and interactions that athletics department staff members can have with prospective student-athletes to ensure fair recruiting practices and to maintain the integrity of college athletics.

Promoting a prospective student-athlete's team or coach can be seen as providing an unfair advantage to that individual or group, which is contrary to NCAA regulations. Similarly, promoting an athletics facility that is primarily used by prospective student-athletes could imply a level of endorsement or favoritism that the NCAA aims to prevent to level the playing field in recruiting.

These restrictions are in place to avoid any actions that would unduly influence a prospective student-athlete's decision-making process regarding their college choice, ensuring that all candidates are evaluated based on their individual merit rather than external promotions or endorsements.