Question

A computer uses passwords that consist of the 26 letters (a-z) and the 10 numbers (0-9). The lettersare not case-sensitive (i.e., there is no difference between upper- and lower-case).(a) How many different passwords are possible if exactly 6 characters (letters or numbers) are required?

Answer 1

Answer:

$36^6=2 176 782 336$

Step-by-step explanation:

If the password was one character long, you would have 36 options.

If the password was two characters long, you would have 36*36 (a+ any random letter, or b+ any random letter. etc.) options

If the password was three characters long, you would have 36*(36*36) options (a two characters password, plus another character).

...

At six characters, you have 36*36*36*36*36*36, or $36^6$ that is 2 176 782 336