Question

In a class of $35$ strudents $24$ 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?

Answer 1

Given data:
Number of students who like to play cricket $=n\left(C\right)=24$
Number of students who like to play football $=n\left(F\right)=16$
Number of students who like to play cricket or football $=n(C\cup F)=35$

Solve for $n(C\cap F)$
$\because n(C\cup F)=n\left(C\right)+n\left(F\right)-n(C\cap F)$
$\Rightarrow 35=24+16-n(C\cap F)$
$\Rightarrow n(C\cap F)=40-35$
$\Rightarrow n(C\cap F)=5$

Final answer: $5$ students like to play both games.