Hi Joe,
Thanks for posting! Per Engineering.
If you want the total number of classes in a classified file, then same can be seen through Raster > Statistics tool.
If you want the number of cells which are covered by each class then that information can also be accessed through statistics tool.
It seems that you are interested in second option.
If you open any classified file (grid) In MapInfo Pro Advanced and under Raster > statistics tool, then by clicking on the graph tab in statistics tool you can get this information.
Screenshot for reference.
Hope this is what you are looking for.