Suppose that a data warehouse for Big_University consists of the four dimensions student, course, semester, and instructor, and two measures count and avg_grade. At the lowest conceptual level (e.g., for a given student, course, semester, and instructor combination), the avg_grade measure stores the actual course grade of the student. At higher conceptual levels, avg_grade stores the average grade for the given combination.

a. Draw a snowflake schema diagram for the data warehouse.

b. Starting with the base cuboid [student, course, semester,instructor], what specific OLAP operations (e.g., roll-up from semester to year) should you perform in order to list the average grade of \(C S\) courses for each Big_University student.
c. If each dimension has five levels (including a11), such as "student \(<\) major \(<\) status \(<\) university < a11," how many cuboids will this cube contain (including the base and apex cuboids)?