To determine how many unique license plates can be created using a combination of 3 letters followed by 2 digits, we need to break this down into two parts: the letters and the digits.
Step 1: Calculate the number of combinations for the letters.
The English alphabet consists of 26 letters. When forming a license plate with 3 letters, each position can be filled by any of the 26 letters, and since repetition is allowed, we can use:
Number of combinations for letters = 26 x 26 x 26 = 263.
Calculating this gives:
263 = 17,576 unique combinations of letters.
Step 2: Calculate the number of combinations for the digits.
The digits can range from 0 to 9, providing 10 possible choices for each digit. For a license plate consisting of 2 digits, we also allow repetition:
Number of combinations for digits = 10 x 10 = 102.
Calculating this gives:
102 = 100 unique combinations of digits.
Step 3: Combine the two results.
To find the total number of unique license plates, we multiply the number of letter combinations by the number of digit combinations:
Total unique license plates = Number of letter combinations x Number of digit combinations.
Therefore:
17,576 (letter combinations) x 100 (digit combinations) = 1,757,600 unique license plates possible.
Conclusion:
In summary, you can create a total of 1,757,600 unique license plates consisting of 3 letters followed by 2 digits.