You can do this by taking 4C2 - 1.

Or, this is a pretty easy problem to just go through the combinations. Given the choices, you have at most 6 combinations to identify.

Here are the combos:

1,2

1,3

1,4

2,3

2,4

3,4

Look six combinations, but don't count (2,4). So 5 different subsets.