As mentioned by the existing answer, it is in princple not appropriate to use logistic regression in this kind of situation. It could be that you would still get decent results, but I would go for a different approach.
I assume you will find an extensive literature on this topic, if you look into statistical models for university/college admission.
One idea would be the following: Assume that there is some kind of implicit "qualification score" that is formed by those selecting people. Let's assume that it's a continuous number (e.g. for a university entrance some kind of academic aptitude score plus bonus points for extracuricular activities) and the score everyone gets is unchanged depending on who else is applying (i.e. this would assume that there's no attempt to get the number of people with certain backgrounds balanced in any other way than giving some groups bonus points on the overall score). In that case you could look at this as observing that the successful applicants had higher qualification scores than those that were not successful. However, you do not know how the successful and unsuccessful ones were ordered - although you might learn a little bit about this if e.g. some successful applicants do accept the offer and the next most suitable ones get an offer.