Assume that you have a total of 11 people on the board: 4 out-of-state seniors, 3 in-state seniors, 2 out-of-state non-seniors, and 2 in-state non-seniors. University rules require that at least one in-state student and at least one senior hold one of the three offices. Note that if individuals change offices, then a different selection exists. In how many ways can the officers be chosen while still conforming to University rules?
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 you have a total of 11 people on the board: 4 out-of-state seniors, 3 in-state seniors, 2 out-of-state non-seniors, and 2 in-state non-seniors. University rules require that at least one in-state student and at least one senior hold one of the three offices. Note that if individuals change offices, then a different selection exists.
In how many ways can the officers be chosen while still conforming to University rules?
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