Question

A user’s password to access a computer system consists of 3 letters followed by 2 digits. How many different passwords are possible?

Answer 1

Case 1: password is not case sensitive;

N = 26×26×26×10×10 = 1757600 possible ways

Case 2: password is case sensitive;

N = 52×52×52×10×10 = 14060800 possible ways

Explanation:

We have 26 letters of the alphabet, and 10 digits.

There are two forms to this question;

1. Assuming that the password is not case sensitive (i.e capital A and lower case a are treated as the same) then the number of possible different passwords can be given as;

So we have 26 options for each letter and 10 options for each digit)

N = 26×26×26×10×10 = 1757600

2. When the password is case sensitive that is A and a are treated as different characters, then we have 26 possible upper case letters and 26 possible lower case letters making 52 options for each letter. So the number of possible distinct passwords is;

N = 52×52×52×10×10 = 14060800

Answer 2

26*26*26 = 17576 ways to select 3 letters

10*10= 100 ways to select 2 numbers

So then the total number of ways are:

`26^3 *10^2 = 1757600` possible ways

Explanation:

For this case we assume that we have 26 letters from A to Z and 10 numbers from 0 to 9 .

And we want to calculate the number of possible passwords possible if the password consists of 3 letters followed by 2 digits.

And for this case we can use the multiplication principle of combinatories, since we don't have any restriction about the letters of the numbers we can have repetition of letters or numbers.

For the number of possible letters:

26*26*26 = 17576 ways to select 3 letters

10*10= 100 ways to select 2 numbers

So then the total number of ways are:

`26^3 *10^2 = 1757600` possible ways