Total Number of student is 300.
n(M-600) = 100, n(C-600) = 200, n(E-600) = 60 (Given data in question)
We need to find max((M-600)∩(C-600)∩(E-600)).............................?
n(M-600)+n(C-600)+n(E-600) = 100+200+60 = 360 (Every one has taken at-least one subject) then 360 - 300 = 60 (Remeber)
we have 60 people who has been enrolled for more than one subject in M.tech Program.
so 60 / 2 = 30 (To maximize the 3 subject student we can enroll 30 student max for all three subject).
Please comment if it's easy to understand i will upload the pictorial representation with some small example.