A Web site requires that users create a password with the following specificatio

Question

A Web site requires that users create a password with the following specifications:

• length of 8 to 10 characters; • includes at least one special character among the following 24 characters: !, @, #, $, %, ^, &, *, (, ), +, =, {, }, |, <, >, , _, -, [, ], /, ?

• no spaces; • may contain numbers 0, 1, . . . , 9, and lower and upper case letters (a–z, A–Z) (note that there are 26 letter is the alphabet);

• the password is case-sensitive.

(a) How many passwords are there?

(b) How long would it take to try all passwords if a password can be tested in 1 microsecond? Note that microsecond is equal to one millionth of second.

Explanation / Answer

Number of option for special character = 24

Number of options for any other character = 10+26+26+24 = 86

Number of characters that are not special characters = 10=26+26 = 62

a) total number of passwords = 868 - all characters are not special characters

= 868 - 628

= 2.774x1015

b) Time required to try all passwords if a password can be tested in 1 microsecond = 2.774x1015/106

= 2.774x109 seconds

= 32104.62 days

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