what password can be made using A,E,I,O,U with at most 3 characters and at least 1

Question

 The club must select a password for their university internet account. If the password must be at least one character long and at most 3 characters long and only consist of the vowels (a, e,i,o,u), how many passwords are possible? (assume that vowels can be repeated in a password)

Answer 1

There will be three types of passwords. Only one letter, two letters, and three letters. We'll figure out each individually and then use addition.

1 letter passwords are easy: there are 5.

Let's now examine how two letter passwords work. First, look at all passwords that start with "A". We have AA, AE, AI, AO, and AU. For each starting letter, there are five possible combinations. So, 5 x 5 = 25.

The same pattern remains in tact for 3 letter passwords, so 5 x 5 x 5 = 125

125 + 25 + 5, so 155 possible passwords.