Question 167
30 students took a test consisting of three problems. Problems were worth 1, 2, 4 points respectively if solved correctly, and no partial credits were given for any of the problems. Suppose that for each of the problems there were 10 students answering it correctly. How many different possibilities were there for the set of 30 grades obtained by students? We consider two sets of 30 grades to represent a same set if one is a permutation of the other.