How many students registered for each course?
select count(*) from student_course_registrations group by course_id
How many courses did each student register for?
select count(*) from student_course_registrations group by student_id
Give the student id as well.
select t1.student_id, count(*) from students as t1 join student_course_registrations as t2 on t1.student_id = t2.student_id group by t1.student_id