The serial numbers of a manufactured computer chip contain 5 characters, with the following restrictions. Each character is either a capital letter or a numerical digit (0 through 9). The first two characters must be letters. The last three characters must be digits. No character may be repeated. How many different license plates are possible with these rules? Note: Along with your numerical answer, explain the calculation used to find it.
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 serial numbers of a manufactured computer chip contain 5 characters, with the following restrictions.
- Each character is either a capital letter or a numerical digit (0 through 9).
- The first two characters must be letters.
- The last three characters must be digits.
- No character may be repeated.
How many different license plates are possible with these rules?
Note: Along with your numerical answer, explain the calculation used to find it.
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