How many license plates using 8 digits can a certain state issue if the following is true? (a) Repetition of digits is permitted. (b) Repetition of digits is not permitted. (c) Suppose the population of this state was 1,952,024. Why do you think this state allows repetition of digits in its license plates?
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.
How many license plates using 8 digits can a certain state issue if the following is true?
(b) Repetition of digits is not permitted.
(c) Suppose the population of this state was 1,952,024. Why do you think this state allows repetition of digits in its license plates?
- The population is greater than the number of licenses without repeating digits, so there would not be enough license plates for this population.
- The population is greater than the number of licenses with repeating digits, so there would not be enough license plates for this population.
- The population is greater than the number of licenses with repeating digits, so there would be enough license plates for this population.
- The population is less than the number of licenses without repeating digits, so there would not be enough license plates for this population.
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