In Harry Potter, how many courses do Hogwarts students have to study? What is the difference?

Required courses: Curse, Transfiguration, Potions, Herbology, Defense against the Dark Arts, Magic History, Flying (Grade One), Astronomy.

Elective courses: ancient magic writing, divination, arithmetic divination, protection of magical creatures, muggle research.

Theoretically, two elective courses are needed, and flying seems to be only available in 1 grade. That is to say:

There are 8 doors in Grade One, 7 doors in Grade Two, and 7+2+X doors in Grade Three to Grade Five. Only students who have passed the O.W.Ts in the fifth grade can continue the courses in the sixth and seventh grades.