David R.

asked • 05/14/16

how many passwords are possible if three letters are followed by two digits

 probabilities and statistics

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Charles S. answered • 05/14/16

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Please correct me if I am wrong. Given 26 letters and 10 digits I thought the answer should be
 
 
263 * 102
 
If capital letters are allowed I was under the impression that the number of passwords should be
 
523 * 102
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David W.

"if three letters are followed by two digits" sounds like a Permutation, not Combination.  That is, passwords like AAB110 and ABA101 are both allowed (with duplicate letters/numbers) and are different from each other (even though they contain the same letters and the same numbers).
 
So, reading the problem statement as, "any three letters followed by any two digits," means that there are 263*102=1,757,600 possible passwords (note that passwords like OOO000 and others might be confusing or disallowed for other reasons, like custom license plates that are offensive).
 
Security note:  If these are computer passwords and another computer is simulating the user and the computer with the password allows 100 attempts per second (or you somehow have a copy of the password file), you can guarantee cracking the password in a maximum of 4.9 days (note: running a PC continuously for that long doesn't cost much).  This is why "strong passwords" are recommended.
 
 
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05/14/16

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