u/Alternative-Ad-2376

The answer is supposedly C), but I have no idea why. When I count, I get:

23 Rectangles (8 single, 5 2-clumps horizontally, 4 2-clumps vertically, 4 clumps of 3, 1 clump of 4, and 1 clump of 6)

23 Triangles (12 single, 4 2-s in the center, 4 4-s in the center, 1 big triangle at the top, and 2 halves of the big triangle)

I'm not sure I've counted correctly all of them (there might be more), but 23 * (4+3) = 23 * 7 = 161, which is greater than 157, the answer.

Is the question wrong? How would I use combinatorics to solve it? (I still don't understand how the combinatorics would work for this)