There are 200,000 different student on an average in 20 years .

each student has unique student id .

The table has primary index on student_id which means it has 200000 tuples .

So total number of levels $\left \lceil \log_{101}200000 \right \rceil=3$

alternatively ,

0^{th} level has $1$ node.(root)

1^{st} level has $101$ node .

2^{nd} level has $101*101$ node

3^{rd} level has $101*101*101$ node.

So, $1+101+101*101+101*101*101$ this will include all the rows which need at least 3 levels considering root at 0^{th} level .

(But I think the key should be combination of student_id + Course_Id as 40 course they can take which increases rows )