Using the arrangements formula, it is found that 5040 different passcodes can be built from the letters {A, B, C, ., *, 1, D}.
What is the arrangements formula?
The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, the letters are given by:
{A, B, C, ., *, 1, D}.
Hence there are 7 symbols, which means that the number of passwords is given by:
[tex]A_7 = 7! = 5040[/tex]
More can be learned about the arrangements formula at https://brainly.com/question/25925367
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