I have this combinatorial assignment problem: K candidates apply for a job. There are R referees available to review their resumes and make a recommendation. Suppose that we would like M referees to review each candidate (M < R). How would you assign candidates to referees (or, conversely, referees to candidates)? There are two important cases: (a) K > (R choose M) and (b) K < (R chooses M). Case (a) actually reduces to case (b), so we only have to consider case (b).
Of course, there are some constraints that make the assignment a bit challenging. We would like to have an even distribution of the number of candidates reviewed by each referee. We would also like to have some randomness or "mixing" in the assignment such that it is probable for any candidate to be assigned to any M-plet of referees. Is this an instance of a well known problem in combinatorics? Any hints or references to algorithms is appreciated.