Number of ways to divide variables into two categories

Question

I'm looking for a possible solution to find out the maximum number of combinations that can be derived from the given variables. If I'm not mistaken, I think permutations and combinations is the way to go for solving this puzzle.

Question

There are 4 variables:

11
01
10
00

I want to know the total number of combinations using the above variables when divided into two categories.

Example 1

A = 11 - 01
B = 10 - 00

The above makes it 1 set of combination. So in total how many variations can be derived?

Example 2:

A = 01 - 11
B = 10 - 00

and so on..

Answer 1

According to your examples 1 and 2, order within groups matters. If so, then there are $4! = 24$ such ordered partitions. Indeed, they are all generated by ordering the four elements in some way ($4!$ ways to do so) and drawing a line between first two and the last two.