It would be possible to limit the student option but how you will do this depends on what you would like the user experience to be like. Will you have special registration codes for the students to use to register? This is the first step, you must determine what criteria you would like to use to determine if the user is a valid student or not.
Once you know how you would like to make this determination you can then proceed to implement the solution. Please describe how this should work from the perspective of the user or student and we will gladly help you with whatever we can.