How many different committees are possible?
Permutations and Combinations
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.
![A committee is to consist of a chair, four hagglers, and five do-nothings. The committee is formed by choosing randomly
from a pool of 12 people and assigning them to the various "jobs."
(a) How many different committees are possible? HINT [See Example 5.]
committees
(b) Norman is eager to be the chair of the committee. What is the probability that he will get his wish? (Round your
answer to two decimal places.)
(c) Norman's girlfriend Norma is less ambitious and would be happy to hold any position on the committee provided that
Norman is also selected as a committee member. What is the probability that she will get her wish and serve on the
committee? (Round your answer to two decimal places.)
(d) Norma does not get along with Oona (who is also in the pool of prospective members) and would be most unhappy if
Oona were to chair the committee. Find the probability that all Norma's wishes will be fulfilled: She and Norman are
on the committee, and it is not chaired by Oona. (Round your answer to two decimal places.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a1e355d-b960-42c6-9d6f-99705d62e1aa%2F99c47107-033d-4acb-b204-01512b5cda1d%2Fdi0ntqi2t_processed.jpeg&w=3840&q=75)
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