The Event Type defaults to Family Enrollment, however, you can change this so that Students can enroll. In the Event Type Summary tab, set Default Allow Enrollment For: to Student to allow students to enroll (each student filling 1 event opening). If you want the event fee to post automatically, you may also want to consider changing Post Event Fee on Reg? to Student as well. Be sure to Save Changes.
It's also possible to set an Event Type the Default Allow Enrollment For: one way but set a specific date of that Event Type another way.
Example: An Event Type is created with the Default Allow Enrollment For: set to Family; however one Date in this Event Type is set to Student.