If I am understanding you correctly, the number of ways to arrange 2 objects 3 at a time is , not 4.

You are using A and B:

AAA, BBB, BBA, BAB, ABB, AAB, ABA, BAA

If you want to see how many are possible using 3 different items 3 at a time is:

And so on.

How many ways can you arrange 2 objects 10 at a time:

Is that what you were getting at?.