So, there are alot of questions about tiling in this forum but I could not find this exact question.
I am trying to find out the number of possible "tile configurations" in an $n\times n$ grid where the tiles are $1\times 1$ and there are k less than or equal to $n^2$ of them. I have link down below with the "tile configurations" for a $2\times 2$ grid.
I don't know, but I feel like I am missing some simple way of approaching the problem. I've been trying to frame it in the context of the combination formula, but I feel like my intuition is lacking... Anyway, if someone could give me a hint that would be much appreciated.