This is a Finite Mathematics PROBABILITY PROBLEM.

David:

Essentially, the question appears to be asking how many "combinations" of 8 alpha/numeric characters can be formed from a set of 15 alpha/numeric characters (A, B, C, D, E, F, G, H, I, J, 2, 3, 4, 5, 6).

When dealing with "combinations" in math it is broken down into two different terms: combinations - the order
doesn't matter (ABCDEFGH is the same as HGFEDCBA) and permutations - the order
does matter (ABCDEFGH is not the same as HGFEDCBA). In this case, ABCDEFGH would be a different password than HGFEDCBA, so order
does matter.

Assuming repetition is allowed, for example, a password could be AAAAAAAA, or 22334455, etc., to solve we need the permutation formula allowing for repetition. If we have n things to choose from, then we have n choices each time and when choosing r of them the number of permutations are n*n*... (r times) or n

^{r}.n

^{r}= 15^{8}= 2,562,890,625There are 2,562,890,625 8 alpha/numeric character/symbol passwords using the letters A to J and numbers 2 to 6.

Let me know if you have any questions on this.

Regards,

Brian

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