Question $12(12$ points$)$

In Spring $2025,$ the department is planning on offering a new course CSE$4366.$

This course has $4$ prerequisites: CSE$1320,$ CSE$2315,$ CSE$3315$ and CSE$4308.$ There are $40$ students interested in taking this class and have met one or more of the prerequisites. Of those, $25$ have taken CSE$1320,20$ have taken CSE$2315,10$ have taken CSE$3315$ and $15$ have taken CSE$4308.$ Also, $15$ have taken CSE$1320$ and CSE$2315,8$ have taken CSE$1320$ and CSE$3315,5$ have taken CSE$1320$ and CSE$4308,4$ have taken CSE$2315$ and CSE$3315,6$ have taken CSE$2315$ and CSE$4308$ and $2$ have taken CSE$3315$ and CSE$4308.$ Finally, $6$ have taken CSE$1320,$ CSE$2315$ and CSE$3315,5$ have taken CSE$1320,$ CSE$2315$ and CSE $4308,5$ have taken CSE$1320,$ CSE$3315$ and CSE$4308$ and $4$ have taken CSE$2315,$ CSE$3315$ and CSE$4308.$ How many students are actually eligible to take the class.