A motorcycle licence plate consists of two or three letters followed by four digits. How many licence plates can be made?

26^2 * 10^4 + 26^3 * 10^4 = 27 * 26^2 * 10^4 = 182520000

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To calculate the total number of license plates that can be made, we need to consider the number of possibilities for each component.

1. First, let's consider the letters. Assuming a standard Latin alphabet with 26 letters, there are 26 options for the first letter, 26 options for the second letter, and 26 options for the third letter (if the plate has three letters). Therefore, the number of possibilities for the letters is 26 x 26 x 26 = 17,576.

2. Next, let's consider the digits. Since there are four digits on the license plate, and each digit can range from 0 to 9, there are 10 options for each digit. Therefore, the number of possibilities for the digits is 10 x 10 x 10 x 10 = 10,000.

3. To find the total number of license plates, we multiply the number of possibilities for the letters by the number of possibilities for the digits: 17,576 x 10,000 = 175,760,000.

Therefore, a total of 175,760,000 license plates can be made.

To find out the number of possible license plates that can be made, we need to calculate the total number of combinations for each part of the license plate.

1. Letter Combinations:
Since the license plate can consist of two or three letters, we need to calculate the number of combinations for each possibility.

For two letters (XX format):
There are 26 letters in the English alphabet, so we have 26 choices for the first letter, and the same for the second letter. Thus, there are 26 x 26 = 676 combinations for the XX format.

For three letters (XXX format):
Again, we have 26 choices for each letter position. So, the number of combinations for the XXX format is 26 x 26 x 26 = 17,576.

2. Digit Combinations:
There are four digits in the license plate. Each digit can be in the range of 0 to 9. So, we have 10 choices for each digit position. Therefore, the number of combinations for the four-digit part is 10 x 10 x 10 x 10 = 10,000.

Now, we can calculate the total number of license plates by multiplying the letter combinations with the digit combinations for each format:

For the XX format: 676 (letter combinations) x 10,000 (digit combinations) = 6,760,000 license plates.

For the XXX format: 17,576 (letter combinations) x 10,000 (digit combinations) = 175,760,000 license plates.

Therefore, the total number of license plates that can be made is 6,760,000 + 175,760,000 = 182,520,000 license plates.