The university senate needs to select an eight-person committee from a pool of 20 faculty members consisting of 14 professors and 6 instructors. How many ways can they select a group of 8 faculty members to form the committee if they must choose exactly 5 professors?
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 university senate needs to select an eight-person committee from a pool of 20 faculty members consisting of 14 professors and 6 instructors.
How many ways can they select a group of 8 faculty members to form the committee if they must choose exactly 5 professors?
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