This one has really been troubling me. The question is:
A computer program requires a password of at least 6 but no more than 8 characters. All letters (of the English alphabet, not case sensitive) and digits (0 to 9) may be used. The password must contain at least one digit and one letter. How many different passwords are possible?
I used the indirect method for each case and got down to:
Case 1: 6 character password
36^6 - (26^6 + 10^6)
Case 2: 7 character password
36^7 - (26^7 + 10^7)
Case 3: 8 character password
36^8 - (26^8 + 10^8)
And then I added all the cases together. Is that correct?