Question

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

Answer 1

Let C=C= set of students who like cricket F=F= set of students who like football
Then n(Cuf)=35,n(C)=24,n(F)n(Cuf)=35,n(C)=24,n(F)
=16n(CnF)=n(C)+n(F)−n(CuF)=16n(CnF)=n(C)+n(F)−n(CuF)
=24+16−35=5=24+16−35=5
∴∴5$ students like to play both games.