

Permutations
Name: Ed L.
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: N/A
Question:
Suppose the following:
S1 = A..Z (26)
S2 = a..z (26)
s3 = 0..9 (10)

62
If I have an 8 character string, how many combinations of the above are
possible?
I think the answer would be 218,340,105,584,896 or 62**8
Suppose that we introduce a rule which states that at least one of the
eight characters must be a number, one must be an upperace letter, and one
must be a lowercase letter. The position does not matter. I think the
answer would be 16,101,950,655,232 or (62**5) x 26 x 26 x 10
I have been repetedly assured my calculation is incorrect because it fails
to take into account the exact position for each mandated character (even
though the rule itself does not care); but no one can offer me a formula
to show what the correct answer would be. I do not mind being wrong, but I
sure would like to know what the correct answer is and the formula
used to arrive there.
Replies:
I am going to assume that when you say "...one must be a...", you mean
"...at least one must be a..." for letters as well as for numbers.
It is probably easiest to just subtract the number of forbidden strings:
62**8  52**8  36**8  36**8
Tim Mooney
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Update: June 2012

