Final answer:
This math problem deals with calculating permutations, specifically how many different nine-letter passwords can be created from a set of 12 unique characters. The correct answer is found using the permutation formula, resulting in 79,833,600 different possible passwords.
Step-by-step explanation:
The question is asking how many different nine-letter passwords can be created using a given set of letters and numbers. This is an example of a permutation because the order of the letters and numbers in the password does matter. In our case, we have twelve unique characters (A, B, C, D, E, F, G, 1, 2, 3, 4, 5) to choose from and we want to form a nine-character password.
To calculate this, we use the permutation formula nPr = n! / (n-r)!, where n is the total number of items to choose from, and r is the number of items we are selecting. With 12 characters to choose from and selecting 9, it would be calculated as 12P9 = 12! / (12-9)! = 12! / 3!
As a result, 12P9 is equal to 79833600 different possible nine-letter passwords that can be formed with these characters.