Question 155471
A password consists of 11 characters. A user must select a password consisting of AT LEAST 2 lower case letters, 2 upper case letters, 2 digits AND 2 special characters. How many passwords exist? 
#lower case letters = 26
#upper case letters = 26
#digits = 10
#special characters = 32 
--------------------------------
Comment: I'm assuming repetition is not allowed.
--------------------------------
Pick 2 lower case: 26C2 leaving 24
Pick 2 upper case: 26C2 leaving 24
Pick 2 digits: 10C2 leaving 8
Pick 2 special characters: 32C2 leaving 30

Pick 3 of anything without repeating previous selections 86C3
-----------------------------------
Multiply all those picks, then multiply by 11! to get all the arrangements.
I get 9.410585 x 10^16
============================
Cheers,
Stan H.