Counting A computer hacker is trying o breakinto a computer system by guessing h

Question

Counting A computer hacker is trying o breakinto a computer system by guessing he system administrator's password. The hacker can 15 passwords a minute but he i sunsuccessiul more than 12 minutes a day, he will get caught. If he limits his attempts to at most 12 minutes each day, he will not get caught. The hacker knows that the administrator's password is at least 6 and at most 10 characters long, does not contain any character that is not a number, an uppercase letter, or a lowercase letter (no special characters such as spaces, punctuation marks, dollar signs, etc.), and that the first character is a letter. Case matters, and characters can be repeated Problem 10 How many passwords are there that start with a letter, contain only numbers and upper and lowercase letters, and are at least 6 and at most 10 characters long? (Q10)

Explanation / Answer

Problem 10

Here number of such passwords are there are ;

Here passwords start with a letter which can be an upper case or lower case letter.

So, at least 6 or at most 10 character are there.

If there are 6 character in passwords. number of password = (26 * 2) * (26 * 2 + 10)5= 52 * 625

Here as for first character there are 52 possibilities as (Aa,Bb...Zz etc) and for rest of the characters digits from 0 to 9 shall also be incuded/

if 7 characters in passwords, number of passwords = 52 * 626

if 8 characters in passwords, number of passwords = 52 * 627

if 9 characters in passwords, number of passwords = 52 * 628

if 10 characters in passwords, number of passwords = 52 * 629

Total number of such passwords =   52 * [625 + 626 +  627 +  628 + 629] =

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