A town is forming a committee to investigate ways to improve public safety in the town. The committee will consist of three representatives from the seven-member town council, three members of a five-person citizens advisory board, and two of the 12 police officers on the force. How many ways can that committee be formed?
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 town is forming a committee to investigate ways to improve public safety in the town. The committee will consist of three representatives from the seven-member town council, three members of a five-person citizens advisory board, and two of the 12 police officers on the force. How many ways can that committee be formed?
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