Standard automobile license plates in a state display 4 digits (from 0-9), followed by 3 letters (from A to Z).How many different standard plates are possible in this system? (Assume repetitions of letters and numbers are allowed.)There are license plate combinations.
Question
Standard automobile license plates in a state display 4 digits (from 0-9), followed by 3 letters (from A to Z).How many different standard plates are possible in this system? (Assume repetitions of letters and numbers are allowed.)There are license plate combinations.
Solution
To calculate the total number of different standard plates possible, we need to consider the number of possibilities for each digit and letter separately.
For the digits, there are 10 possibilities (0-9) for each of the 4 digits. So, the total number of possibilities for the digits is 10^4 = 10,000.
For the letters, there are 26 possibilities (A-Z) for each of the 3 letters. So, the total number of possibilities for the letters is 26^3 = 17,576.
To get the total number of different standard plates possible, we multiply the number of possibilities for the digits by the number of possibilities for the letters.
So, the total number of different standard plates possible is 10,000 * 17,576 = 175,760,000.
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