A password consists of 4 characters, each of which is either a digit or a letter of the alphabet. Each password must contain at least ONE digit and AT LEAST ONE letter. How many different such passwords are there?
I am not sure how to go about this one. At first I did 4 blank digits: XXXX. I did lowercase and uppercase separately since it doesn't specify above. 36^4=1,569,616 for just digits and lowercase. 14,776,336 for lowercase, uppercase, and digits (62^4).
There are two different ways I can go about this and i'm not sure which one.
Originally I did 26*36*36*10 (reserved a spot for the digit, and one for the lowercase) and got 336,60 which seems a bit low.
Then I took the total and subtracted it from the things it could not be (10^4 for digits, and 26^4 for letters only) and got 1,212,640.
I essentially did the same with uppercase, but wasn't sure if I should use 26^4 twice (for lowercase and uppercase) or use 52^4.
Which method should I be using, and if possible please explain why?