This the problem from the test and I'm stuck at one part.
Matt will arrange four identical, dotless dominoes (shaded 1 by 2 rectangles) on the 5 by 4 grid to the right so that a path is formed from the upper left-hand corner A to the lower right hand corner B. In a path, consecutive dominoes must touch at their sides and not just their corners. No domino may be placed diagonally; each domino covers exactly two of the unit squares shown on the grid. One arrangement is shown. How many distinct arrangements are possible, including the one shown?
So do I just find all the numbers of vertical and horizontal possible and then multiply by the number of arrangements of each, or should I go a different route?