2. A computer password is created to be 6 lower case letters (26 letters for eac

Question

2. A computer password is created to be 6 lower case letters (26 letters for each spot) followed by 2 digits (10 digits for each spot).

a. How many different passwords are possible if each letter may be any lower case letter (26 letters) and each digit may be any of the 10 digits?

b. How many different passwords are possible if each letter may be any lower case letter, each digit may be any one of the 10 digits, but the digit 9 is not allowed to appear twice? Hint: Think of the total number ways a password can be created, and then subtract of the number of ways you are not allowed to create the password.

c. In the setting of (a) you forget your password, but remember that the first three letters are ”abs” in that order. You decide to take a random guess at the remaining characters. What is the probability that you guess correctly?

d. In the setting of (a), how many passwords can you create if you cannot reuse a letter?

Explanation / Answer

Solution:

Given,

A computer password is created to be 6 lower case letters followed by 2 digits

( a )

number of passwords possible with 6 lowercase letters and 2 digits = 266 * 102 = 30897577600

( b )

number of different paswords with 6 lowercase letters and 2 digits but 9 shouldnt included =   266 * 102 - 266

= 266 (102 - 1)

= 30582661824

( c )

number of passwords with starting letters "abs" = 263 * 102

= 1757600

the probability of guessing the password given that first three letters are "abs" = 1 / 1757600 =0.0000005689  

( d )

tatal number of passwords created with out reputaion of letters or digits = 26p6 * 10p2 = 165765600 * 90

= 14918904000

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