The usual size these days is five but six place nosepieces are available and are usually a good deal. If the nosepiece angles the objectives towards the user if is called a front facing nosepiece. If it angles the objectives towards the frame it is called a rear facing nosepiece. Rear facing nosepieces are the easiest to use although they can be more difficult to manufacture. It is easier to put specimens on a microscope with a rear facing nosepiece and it is more difficult to get your fingers on the front of the objectives and dirty them up.
Some frames have the nosepiece permanently mounted to it.
This is to reduce cost and in some cases is a reasonable trade of. Removable nosepieces allow you to put another set of objectives on the microscope very easily. If you are doing a lot of techniques this is a help. Cleaning objectives is also easier with a removable nosepiece. The objectives screw into the nosepiece.