A country has license plates for cars that have 3 letters followed by 3 digits, or 3 digits followed by 3 letters. A second country has license plates with 4 letters followed by 3 digits. Assuming that zero can be the first digit in a 3 digit license number, how many more license plates can be made using the 4 letter, 3 letter format that can be made with the 3 and 3 format.
(Please reply back)
To get the answer to this question, we need to calculate the number of license plates that can be made using each format and then compare the two.
In the first country, where the license plates have the format 3 letters followed by 3 digits or 3 digits followed by 3 letters, there are 26 possibilities for each letter (assuming only uppercase letters are used) and 10 possibilities for each digit (0-9). Since there are 3 spots for letters and 3 spots for digits, the total number of license plates that can be made using this format is calculated as follows:
(26 * 26 * 26) + (10 * 10 * 10) = 17,576 + 1,000 = 18,576
In the second country, where the license plates have the format 4 letters followed by 3 digits, there are still 26 possibilities for each letter and 10 possibilities for each digit. However, since there are now 4 spots for letters and 3 spots for digits, the total number of license plates that can be made using this format is calculated as follows:
26 * 26 * 26 * 26 + 10 * 10 * 10 = 456,976 + 1,000 = 457,976
To find the difference in the number of license plates that can be made using the 4-letter, 3-digit format compared to the 3-letter, 3-digit format, we subtract the number of license plates from the first country from the number of license plates from the second country:
457,976 - 18,576 = 439,400
Therefore, there are 439,400 more license plates that can be made using the 4-letter, 3-digit format compared to the 3-letter, 3-digit format.
Well, when it comes to license plates, you could say it's like a game of Scrabble on wheels! Now, let's do some License Plate Math, shall we?
In the first country, with the 3 and 3 format, we have 26 choices for each letter and 10 choices for each digit. So, we have a total of (26^3) * (10^3) license plates.
In the second country, with the 4 and 3 format, we have 26 choices for each letter, making it a total of 26^4 * 10^3 license plates.
Now, let's find the difference! By subtracting the number of license plates in the 3 and 3 format from the 4 and 3 format, we get (26^4 * 10^3) - (26^3 * 10^3). And voila! There's your answer! Maybe not as exciting as a clown car, but is there anything more thrilling than License Plate Math?
To find out how many more license plates can be made using the 4 letter, 3 digit format compared to the 3 letter, 3 digit format, we need to calculate the difference in the number of combinations for each format.
For the 3 letter, 3 digit format:
- There are 26 options for each of the 3 letters (A-Z), so there are 26^3 = 17,576 possible combinations.
- There are 10 options for each of the 3 digits (0-9), so there are 10^3 = 1,000 possible combinations.
- Therefore, there are a total of 17,576 * 1,000 = 17,576,000 possible combinations for the 3 letter, 3 digit format.
For the 4 letter, 3 digit format:
- There are 26 options for each of the 4 letters (A-Z), so there are 26^4 = 456,976 possible combinations.
- There are 10 options for each of the 3 digits (0-9), so there are 10^3 = 1,000 possible combinations.
- Therefore, there are a total of 456,976 * 1,000 = 456,976,000 possible combinations for the 4 letter, 3 digit format.
The difference in the number of possible combinations between the two formats is:
456,976,000 - 17,576,000 = 439,400,000
Therefore, there are 439,400,000 more license plates that can be made using the 4 letter, 3 digit format compared to the 3 letter, 3 digit format.
1st country: (26^3 * 10^3)*2
2nd country: 26^4 * 10^3
now just subtract