One professor grades homework by randomly choosing 5 out of12homework problems to grade.

(a)How many different groups of 5 problems can be chosen from the12problems? (Enter an exact number.)

groups

(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? (Enter a number. Round your answer to four decimal places.)

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

groups

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