All poor second-year students majoring in public administration at a university have applied for student loans. All the students who applied for student loans paid their tuition fees. Some students  in public administration save money by tutoring after school. Only when all the tuition fees are paid can the university enroll its students. The university's business administration students also do after-school tutoring, but some do not pay full tuition.
Therefore, which of the following must be false?
Poor students majoring in public administration at the university were successfully enrolled.