characters - note these are based on appearance alone, rather than cameo
Batman 1
Joker 2
Poison ivy 3
Scarecrow 4
Harley Quinn 5
Killer Croc 6
Zasz 7
The Riddler 8
(I know the numbers slope down inexorably, its quite hard to keep in a straight line when not writing them on paper)
the maths stuff;
8 characters/ 4 characters per logo
combinations
1,2,3,4
2,1,3,4
3,2,1,4
4,3,2,1
5,6,7,8
6,5,7,8
7,6,5,8
8,7,6,5
there are more but it becomes increasingly mind boggling or compl