Co-workers are required to create 6-character long passwords. The letters must be from lowercase letters or digits. Each password must start with a lowercase letter and end with a digit and contain at most 2 digits. How many valid passwords are there?
Is my answer correct? What I'm doing wrong if not? $$26 \cdot 36^3 \cdot 10 - 36^2 + 26^2$$
Just consider two cases
Case 1, only one digit at end : $\;26\cdot36^4\cdot10$
Case 2, an extra digit somewhere in the middle:$\;26\cdot36^3\cdot\binom41\cdot10\cdot10$
Add up