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How many different driving licenses numbers in my imaginary land are there if the length of driver license numbers should be 9 characters, start with A, and consist of six capital letters and three different (non-repeating) numbers with numbers standing together. Example: A145BSUAJ, AS623NEEF are valid and AS1H45BAI is not, because 145 are not together

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Final answer:

In your imaginary land, there would be 308,915,776,000 different driver's license numbers if the license numbers should be 9 characters long, start with A, and consist of six capital letters and three different numbers with the numbers standing together.

Step-by-step explanation:

In your imaginary land, if the driver's license numbers should be 9 characters long, start with A, and consist of six capital letters and three different numbers with the numbers standing together, we can calculate the number of different license numbers using combinatorics principles.

There are 26 ways to choose the first letter (A-Z).

There are 26 choices for each of the next six letters (A-Z).

For the three numbers, we have 10 choices for the first number (0-9), 9 choices for the second number (excluding the first one), and 8 choices for the third number (excluding the first two).

Therefore, the total number of different driver license numbers in your imaginary land would be 26 x 26 x 26 x 26 x 26 x 26 x 10 x 9 x 8 = 26^6 x 10 x 9 x 8 = 26^6 x 7,200 = 308,915,776,000.

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