A car rental agency in a major city has a total of 2200 cars that it rents from three locations: Metropolis Airport, downtown, and at the smaller city airport. Rented From Returned to MetropolisAirport Downtown CityAirport MetropolisAirport 90% 10% 10% Downtown 5% 80% 5% At the beginning of a week, how many cars should be at each location so that the number of cars will be there at the end of the week? Start by writing a system of equations using three variables that represent the amount of rental cars at each airport. Then convert this to an augmented matrix and put it in RREF using your calculator.
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 car rental agency in a major city has a total of 2200 cars that it rents from three locations: Metropolis Airport, downtown, and at the smaller city airport.
| Rented From | |||
| Returned to | MetropolisAirport | Downtown | CityAirport |
| MetropolisAirport | 90% | 10% | 10% |
| Downtown | 5% | 80% | 5% |
At the beginning of a week, how many cars should be at each location so that the number of cars will be there at the end of the week?
Start by writing a system of equations using three variables that represent the amount of rental cars at each airport. Then convert this to an augmented matrix and put it in RREF using your calculator.
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