This is actually a baby puzzle, so to make it more challenging, I decided to find all the combinations without the aid of a computer. Unfortunately, that did not work out to well. All rotations and mirror-imaged solutions have been omitted.
Notice that in a 4x2 section, 2 L-shaped pieces can be placed various ways. The same goes for 2 V-shaped pieces inside a 3x2 area. These extra combinations have been omitted as well. After 3 days I finally gave up, and only ended up with the following incomplete list: