Question

An email account has a 6-character password. The first 2 characters must be numbers from 0-9 and you cannot start with 0 or 1. The last 4 characters must be letters. All of the characters can be repeated.

a) How many passwords are possible?
b) How would making the password case sensitive change your calculations?
c) How many passwords are possible if the first 2 characters can start with 0 or 1?
d) What is the total number of passwords when only numbers are allowed?

Answer 1

There are 45,697,600 possible passwords for the given criteria. Making the password case sensitive would double the number of passwords to 91,395,200. If the first 2 characters can start with 0 or 1, there are 67,600 possible passwords. When only numbers are allowed, there are 262,144 possible passwords.

Step-by-step explanation:

a) To calculate the number of possible passwords, we need to determine the number of choices for each character position and then multiply them together. Since the first 2 characters must be numbers, there are 8 choices (2-9) for each position. Since there are 10 digits (0-9), the total number of choices for the first 2 characters is 8 * 10 = 80. For the last 4 characters, there are 26 choices (A-Z and a-z) for each position. Therefore, the total number of passwords is 80 * 26^4 = 45,697,600.

b) If the password is case sensitive, then the number of choices for the last 4 characters would double because each position can now be represented by either an uppercase or lowercase letter. Therefore, the total number of passwords would be 80 * 26^4 * 2^4 = 91,395,200.

c) If the first 2 characters can start with 0 or 1, then there are 10 choices (0-9) for each position. Therefore, the total number of passwords is 10^2 * 26^4 = 67,600.

d) If only numbers are allowed, then there are 8 choices (2-9) for each position. Therefore, the total number of passwords is 8^6 = 262,144.