We have four categories of students, those who play badminton (let's call this X), football (10), both sports (8), and neither sport (10).
Total students (25) = badminton (X) + football (10) + neither (10) - both sports (8). We subtract those playing both: since they are included in X as well as the 10 football players, they have been counted twice.
X + 10 + 10 - 8 = 25
X = 13, as the number who play badminton.
Remember, we want the number who play badminton only, so we subtract the number who play both badminton and football from the number who play badminton to get our answer: 13 - 8 = 5.
The correct answer is C.
We didn’t know there were so many badminton-playing football players.