In a class, 25 students play cricket, 18 students play football, and 6 students play both. 10 students play neither cricket nor football. What is the total number of students in the class?

Question: In a class, 25 students play cricket, 18 students play football, and 6 students play both. 10 students play neither cricket nor football. What is the total number of students in the class?

Solution:
Let the number of students who play cricket = 25
Number of students who play football = 18
Number of students who play both cricket and football = 6
Number of students who play neither = 10

The number of students who play cricket or football:
n(C ∪ F) = n(C) + n(F) - n(C ∩ F)
⇒ n(C ∪ F) = 25 + 18 - 6
∴ n(C ∪ F) = 37

Now,
Total students = n(C ∪ F) + neither
Total students = 37 + 10
∴ Total students = 47