The Tiny State College Student Advisory Board has rules to the effect that the officers of the board (i.e., Chairperson, Vice-Chairperson, and Treasurer) must always include at least one in-state student and at least one senior. The TSC Student Council consists of 6 members: 1 in-state senior, two in-state students who are not seniors, 1 out-of-state senior, and two out-of-state students who are not seniors. In how many ways can the officers of the Student Advisory Board be selected from these 6 Student Council members if they must obey the rules? Note that if individual members switch offices, this produces a different Board.
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.
The Tiny State College Student Advisory Board has rules to the effect that the officers of the board (i.e., Chairperson, Vice-Chairperson, and Treasurer) must always include at least one in-state student and at least one senior. The TSC Student Council consists of 6 members: 1 in-state senior, two in-state students who are not seniors, 1 out-of-state senior, and two out-of-state students who are not seniors. In how many ways can the officers of the Student Advisory Board be selected from these 6 Student Council members if they must obey the rules? Note that if individual members switch offices, this produces a different Board.
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