One professor grades homework by randomly choosing 5 out of 12 homework problems to grade. (a) How many different groups of 5 problems can be chosen from the 12 problems? (Enter an exact number.) 792 V 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.) 0.0005 (c) Silvia did 7 problems. How many different groups of 5 did she complete? (Enter an exact number.) 19 x 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.) 0.0105

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If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.