help nedeed for a filtering formula

I have a list which has NAMES (of students), MARKS (for each course), PREFERENCES ( of students - names of the courses) and QUOTA( for each course).
I need an array formula to choose a course for each student by considering the following rules.

1. the student with a lower mark for a course comes first
2. if two or more students have the same marks the smaller preference number (for the same course) has the priority (for the same course)
3. number of studenths for any course can not exceed quota given for each course.

there is an attached sample file.

IF YOU HELP, I WILL APPRECIATE YOU.
THANK YOU EVERYBODY.

thank you for your interest.
they are similar but in that post there is only one mark for each student, in this post students have five marks for ecah of their preferences.
So we have to consider each of these marks for each course to determine which student can take which course.

yes you are right.
course a should be given to name5 and name 6.

(I hope) this time sample distribution is true.

name course
name1 c
name2 d
name3 g
name4 d
name5 a
name6 a

sorry how can I attach a new file ?
a.jpg

sorry I could not attach a new file
a.jpg

while startin a new post screen there was a such a button but now in this reply screen i can not see it

editing toolbar is this
b.jpg

ok thank you.
I found it.

sorry you are right again.
it is not allowed to choose the same course multiple times.
so change pref2 for name1 to "h"?

I hope it does not change the result.