A password can be any string of length 7, 8, or 9. Each character in the password can be any capital letter or special character from the set {*, $, &, #, %}. There are no other restrictions on the password. How many possible different passwords are there?

Question

Mathematics

Jonathan

24 March, 02:52

A password can be any string of length 7, 8, or 9. Each character in the password can be any capital letter or special character from the set {*, $, &, #, %}. There are no other restrictions on the password. How many possible different passwords are there?

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Answers (1)

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Yael Golden · Answer 1

744

Step-by-step explanation:

The alphabet has 26 letters. Since each character of the password can be a capital letter or one of the four character of the set {*, $, &, #, %}, then each space in the password has 26+5=31 options to select a character.

a) If the password has length 7, then there are 31*7=217 different passwords.

b) If the password has length 8, then there are 31*8=248 different passwords and,

c) if the password has length 9, then there are 31*9=279 different passwords.

Then the total of different passwords is 217+248+279=744.