A committee of students and teachers is being formed to study the issue of how much they all love math. Sixteen teachers and 35 students have expressed interest in serving on the committee. There must be at least 2 teachers and at least 2 students on the committee. How many ways can a 6 person committee be chosen?
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 of students and teachers is being formed to study the issue of how much they all love math. Sixteen teachers and 35 students have expressed interest in serving on the committee. There must be at least 2 teachers and at least 2 students on the committee. How many ways can a 6 person committee be chosen?
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