Permutations for 6 character password. From lower case letters or digits containing AT LEAST 2 lowercase letters

Question

We are required to come up with a $6-$character password. The password can contain any lowercase character and digits $(0-9)$ with repetitions allowed. Every valid password needs to contain at least $2$ lowercase characters. How many valid passwords are there?.

Here's what I've got so far

1. Total passwords ($x$) = $36^6$
2. Passwords with no letters ($y$) = $10^6$
3. Passwords with one letter ($z$)= $26^1$
4. Valid passwords = $x - (y + z) = 2.2 \times 10^9$

I would just like to know if my approach and the final answer is correct. Thanks in advance guys!