In a class of 35 students, 24 like to play cricket and 16 like to play football. Also, each student likes to play at least one of the two games. How many students like to play both cricket and football?

Solution: Number of students who like to play cricket,$n\left(A\right)=24$
Number of students who like to play football,$n\left(B\right)=16$
As each student likes to play at least one of the two games,
$n\left(A\cup B\right)=35$
Number of students who like to play both cricket and football,
$n\left(A\cap B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cup B\right)=24+16-35=5$