Hi sanemask,
GMAT questions are always carefully worded so that you (as the Test Taker) can determine what the question is asking you to solve for (so you have to think about what information the prompt gives you AND what the specific question asks you for).
In your first example, you're solving for the number of different COMBINATIONS of 2 items from a total of 4 items (so you use the combination formula).
In your second example, you're solving for the number of different ARRANGEMENTS of 3 different items (so you can use a factorial or the permutation formula).
Your third example is about the number of different ARRANGEMENTS WITH DUPLICATES allowed. Since each of the 3 "spots" can be either a "B" or a "G", there are 2^3 possible arrangements.
GMAT assassins aren't born, they're made,
Rich