A randomly selected member of the set of all of 8 character strings which contain at least 2 of [(upper case letter), (lower case letter), (number), or (Symbol)

A randomly selected member of the set of all of 8 character strings which contain at least 2 of [(upper case letter), (lower case letter), (number), or (Symbol)] has more entropy than the a randomly selected member of the set of 8 character strings which contain only lower case letters. However, all bets are off if the respective strings are no randomly selected. 'Passw0rd' is worse than 'xmliicou'.