Case 1: Both join
In case both the students decide to join,
13C8 × 2C2 ways = 13C8 = \(\frac{13!}{8!\space5!}=1287\)
Case 2: In case none of them join,
it will be 13C10 Ways 13C10 = \(\frac{13!}{3!\space10!}=286\)
Total number of cases are = 13C8 + 13C10
1287 + 286 = 1573