Let us solve it using the conventional formula :
(A U B U C) = A + B + C - (A ∩ B) - (B ∩ C) - (C ∩ A) + (A ∩ B ∩ C)
Notice that in this formula,
A means students in Drama club (but not Drama club only).
B means students in Dance club (but not Dance club only).
C means students in Maths club (but not Maths club only).
So, A = students in Drama club ONLY + students in Drama and Dance clubs + students in Drama and Maths clubs - students in all clubs.
A= 60 + 40 + 7 - 2 = 105.
Similarly,
B = 80 + 12 + 40 - 2 = 130.
C = 30 + 7 + 12 - 2 = 47.
Also, Given that (A ∩ B) = 40, (B ∩ C) = 12, (C ∩ A) = 7 & (A ∩ B ∩ C) = 2
Now just substitute these values in the above formula.
(A U B U C) = 105 + 130 + 47 - 40 - 12 - 7 + 2 = 282 - 57 = 225.
But given that 75% of the students are not in any of these clubs ,i.e, 25% of the students are in at least one of these clubs.
0.25 * x = 225 ==> x = 900.
So, Total number of students in the college = 900.