Question 176545: Please Help me solve this question: A particular website requires that users select a password with between 6 and 8 characters (inclusive). Each character can be a lower case letter, an upper case letter, or one of the digits 0,1,2,...,9. A password must start with a letter, and must have at least one digit. A sample password is tIc4SS. How many such passwords are possible.
Thanks
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! OK, so a password can be 6, 7, or 8 characters long.
The first character has to be a letter (could be upper or lowercase), so that makes 52 (2x26) possible choices.
One of the remaining slots must be a digit with 10 possible choices (0-9).
All of the other remaining slots (total of 4,5,6) can either be a digit, an upper case letter, or a lower case letter with 10+2x26=62 possible choices.
Each slot choice is independent so the total number of passwords is the product of each slot’s number of choices.
So for a 6 character password, there is the first letter slot, the digit slot and then there are 4 remaining slots.
N[6]=52*10*62*62*62*62=520*62^4 possible choices.
For a 7 character password, there are 5 remaining slots.
N[7]=52*10*62*62*62*62*62=520*62^5 possible choices.
And finally for an 8 character password, there are 6 remaining slots,
N[8]=52*10*62*62*62*62*62*62=520*62^6 possible choices.
The total number is then the sum of
N[6,7,8]=520*(62^4+62^5+62^6)=3.002E^12
That's a little over 3 trillion possible passwords.
Just to put some sense to that number, say you wanted to break into someone's account.
If you entered 1 password every second, after 1 year of doing it (with no breaks) you'd have only entered 3 million passwords or .001% of the total possible passwords.
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