Are the walls grouped? Looks like you need to select the geometry and intersect faces. Then you should be able to select the ceiling without selecting the face on the top of the walls. But that’s only a guess because we can’t tell how you have the model set up exactly. Share the file to get better information.
Since you are using the free web version of SketchUp I’ll move your thread to the correct category.
As @DaveR says, it depends on grouping and organization, but if that selected face is in the same context as the wall (i.e. you can select faces and edges of the walls at this level), try tracing just one edge of each room’s ceiling and SU will figure out that that room’s ceiling is a face. You can see the selection change when you do this. After that, you can just select and delete the face for each room.
Thanks guys, I managed to group the walls, use the “intersect faces”, and then select each room celling to be removed 
