Question

In a class of 35 students, 24 likes to play cricket, 5 likes to play both cricket and football. Find how many students like to play football ?

Answer 1

Here, let A be the set of students who likes to play cricket and B be the set of students who likes to play football.

As per question: $n(A\cup B)=35$

$n\left(A\right)=24$

$n(A\cap B)=5$

We know, $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$\Rightarrow n\left(B\right)=n(A\cup B)-n\left(A\right)+n(A\cap B)$

$=35-24+5$

$=16$

Hence number of students who like to play football $=16$.