One professor grades homework by randomly choosing 5 out of 14 homework problems to grade. (a) How many different groups of 5 problems can be chosen from the 14 problems?

(b) Probability extension: 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? (Round your answer to four decimal places.)

(c) Silvia did 7 problems. How many different groups of 5 did she complete?

What is the probability that one of the groups of 5 she completed comprised the group selected to be graded? (Round your answer to four decimal places.)