Assume that the committee consists of 14 members including Julie. The same three offices are to be filled. (1) In how many different ways can the offices be filled if each person can hold at most one office? (2) In how many of these ways is Julie the chairperson? (3) In how many of these ways is Julie an officer?
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.
Assume that the committee consists of 14 members including Julie. The same three offices are to be filled.
(1) In how many different ways can the offices be filled if each person can hold at most one office?
(2) In how many of these ways is Julie the chairperson?
(3) In how many of these ways is Julie an officer?
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