I can only try
You’re off to a good start but let me make some corrections.
The center piece is one piece and remains fixed. On a “classic Rubik’s Cube” the orientation of the center faces won’t make a difference. (Had there been any writing or a logo then the orientation would have to be taken into account since the writing (or drawing) must be face up.) Therefore the center piece can be ignored for this problem.
The other mistake is that you are not taking into account the possibility of losing a degree of freedom. If one were to disassemble a Rubik’s Cube and put the pieces together at random- chances are that the resulting cube will have no solution. When assembling the cube most pieces may be placed in randomly but there will be a few that are forced into a specific location or position- hence the loss of a degree of freedom. As a hint: there will be one piece forced into a certain location and two pieces forced in a specific orientation.