A professor grades homework by randomly choosing 5 out of 12 homework problems to grade.

a) How many different groups of 5 are there from the 12 problems?
b) 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?
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.

a) How many different groups of 5 are there from the 12 problems?

The no of ways of choosing 5 out of 12 is 12 C 5 = 792

b) 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?

Total no of ways in which 5 problems can be selected from 12 = 792 (as shown in part a above)
Thus there are 792 sets of 5 problems each
Since the process of selecting the problems is random, the probability of selecting any one set of 5 problems is the same as selecting any other set

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