One professor grades homework by randomly choosing 5 out of 12 homework problems to grade. We want to count how many different groups of 5 Homeworks are possible. a) Is this a permutation or a combinations problem? EXPLAIN VERY WELL. b) How many different groups of 5 problems can be chosen from the 12 problems? EXPLAIN VERY WELL. c) Jerry did only 5 problems of one assignment. What is the probability that the problems he did comprised the group that was selected to be graded? Show all the necessary work to obtain your answer.