The 8 volunteer firefighters devised a plan for teaching basic fire-safety in a small town (population 26,000). They decided that each of them would teach three other people the fire-safety basics. At that point, the teachers would retire but each student would teach three others and then retire. Those students, in turn, would teach three others and then retire. The whole thing would be mandated by the city council, and each person would have a month to fulfill his or her teaching requirement. The firefighters taught the first group of people in the first month. Under this plan, how many months will it take for everyone in town to learn the basics of fire safety?
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 8 volunteer firefighters devised a plan for teaching basic fire-safety in a small town (population 26,000). They decided that each of them would teach three other people the fire-safety basics. At that point, the teachers would retire but each student would teach three others and then retire. Those students, in turn, would teach three others and then retire. The whole thing would be mandated by the city council, and each person would have a month to fulfill his or her teaching requirement. The firefighters taught the first group of people in the first month. Under this plan, how many months will it take for everyone in town to learn the basics of fire safety?
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