We have a force of 14 mentors ready to coach 140 students through the first year of their university studies. Unfortunately we have decided to let the mentees choose their mentors, because we thought it would be best, if each student found the mentor that fit him or her best. But, of course, some mentors are more "friendly" appearing, others maybe a bit intimidating for students right from school (age 17 to 20), and now we have a situation where a handful of mentors each have 15 to 25 students in their group, another handful has around 5, and the last handful have 2 to none.

We understand that our idea to let the students choose their mentors might have been a mistake, but that is what we have and now we would like to try and distribute the students more equally among the mentors.

Is there a constructive way to deal with this situation and get students more evenly distributed now that the damage has been done?  How should we explain the change?