Inclusion-exclusion principle, password combination

Question

I am trying to calculate password of 10 character that must contain at least:

• 1 lower case character (26)
• 1 digit (10)
• 1 special digit (8)

I did this,I just want to confirm I used the principle correctly.

Here is my answer

44^10 - (26 + 10)^10 - (10 + 8)^10 - (26 + 8)^10 + (26^10 + 10^10 + 8^10)

Thanks in advance

Answer 1

Yes; you are applying the principle of counting "including all, excluding (all but 1), and including (all but 2) again" correctly.

$$(26+10+8)^{10} - \big((26 + 10)^{10} + (10 + 8)^{10} + (26 + 8)^{10}\big) + \big(26^{10} + 10^{10} + 8^{10}\big)$$