There are 18 students, three (disjnct) students each from 6 different high schools. there are 6 admissions officers, one from each of 6 colleges. each of the officers successively picks a subset of three of the 18 students to go to their college (once a student is chosen, another college cannot chose her later). how many ways are there to do this so that no officer picks 3 students from the same high