1. (10 points) There are six New York city colleges which will each produce five distinguished Bachelor's degree candidates. There are five trading firms that will hire 7, 7, 6, 6, and 5 graduates respectively. Each firm will hire at most one student from each college: will all the graduates be hired? If so, then give the hiring decisions. If not, then give a proof that no possible combination of hiring decisions results in every graduate receiving a job.