# co.combinatorics – How many passwords can we create that contain atleast one capital letter, a small letter and one digit?

I have a problem in combinatorics.
How many passwords can we create such as:

1. Each password has length $$n$$ when $$nge3$$.
2. Each password must contain at least one capital letter (there are 26 letters in English), and at least one small letter, and at least one digit (there are 10 possible digits)

I tried solving this problem like this:

There are $$62^{n}$$ possible passwords without any restrictions

There are $$2*26^{n}$$ passwords with only capital letters or small letters.

There are $$10^{n}$$ passwords with only digits.

There are $$52^{n}$$ passwords with only capital letters and small letters.

There are $$36^{n}-10^{n}-26^{n}$$ passwords with only capital letters and digits.

There are $$36^{n}-10^{n}-26^{n}$$ passwords with only small letters and digits.

So to get the “right answer” I subtracted all of them from $$62^{n}$$ and got $$62^{n}-52^{n}-2*36^{n}+10^{n}$$

Is this the right method/answer? or did I miss something silly?
I am new to combinatorics and I want to make sure, I am on the right track.