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how many eight symbol computer passwords can be formed using the letters A to J and the digits 2 to 6?

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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 nr.

nr = 158 = 2,562,890,625
There 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.


Hi Brian - very good, clear answer. I notice your first paragraph has "... 15 alpha/numeric characters (A, B, C, D, E, F, G, H, I, J, K, 2, 3, 4, 5, 6)." The 15 is correct, but the list should not have "K".
Best wishes.
Good catch. Yes, the "K" is a typo and should not be there. Thank you.