Total Students who watched Film $= 40$
Let
- $A =$ Students who watched Film "A" alone
- $B =$ Students who watched Film "B" alone
- $C =$ Students who watched Film "C" alone
- $X =$ Students who watched Both Film "A" and "B" but not Film "C"
- $Y =$ Students who watched Both Film "A" and "C" but not Film "B"
- $Z =$ Students who watched Both Film "B" and "C" but not Film "A"
- $O =$ Students who watched all the 3 Films
By Principle of Inclusion and Exclusion, we have
Total Students who watched Film $= A + B + C + X + Y + Z + O$
Now from the Venn diagram it is clear that $13 = A + X + Y + O$
No student watched exactly $2$ films. Hence, $X = Y = Z = 0$
Therefore, $13 = A + 0 + 0 + O$
$\implies 13 - O = A$
Similarly, $B = 16 - O$ and $C = 19 - O$
So, Total Students who watched Film $= A + B + C + X + Y + Z + O$
$\implies 40 = A + B + C + 0 + 0 + 0 + O$
$\implies 40 = A + B + C + O$
$\implies 40 = (13 - O) + (16 - O) + (19 - O) + O$
$\implies 40 = 48 - 2O$
$\implies -8 = -2O$
$\implies O = 4.$
Hence, C is correct.