We study a many-to-one assignment problem, where a set of applicants need to be assigned to a set of schools with limited seats. We formulate distributional objectives by a set of standard axioms. Axiom 1 has two parts. First, the number of applicants of each type at each school should be less than the corresponding quota. Second, whenever the number of applicants of a given type assigned to a school is less than the corresponding reserve, then it should be that no other applicant of that type prefers the school to their own assignment. Axiom 2 requires that whenever a school has available seats, it should be that there is no applicant that prefers that school to their own assignment. Finally, we say that an applicant a violates the priority of another applicant b at school s, if b prefers s to their own assignment, and b has a higher priority at that school than a. In this case, the triplet (a, b, s) is called a priority violation instance. Axiom 3 requires that there are no priority violation instances including two applicants of the same type.