Question

in a class 35 students,24 like cricket 16 like football also each student like to play at least one of two games. how many students like both cricket and football?

Answer 1

Students like cricket + students like football= 24 + 16= 40 
because some students have been counted twice: 1 times in cricket, 1 time in football. 
So students like both criket and football: 40 - 35 = 5 students 
I hope to help you. 

Answer 2

Hey !!

Let X be the sets of students who like to play cricket and Y be the set of students who like to play football.

So, therefore X ∪ Y is the set of students who like to play at least one game, and X ∩ Y is the set of students who like to play both games.

    Given, n(X) = 24 , n(Y) = 16 , n(X ∪ Y) = 35 , n(X ∩ Y) = ?

Using the formula

        n(X ∩ Y) = n(X) + n(Y) - n (X ∩ Y),

we get,        35 = 24 + 16 - n(X ∩ Y)

Thus,

         n (X ∩ Y) = 5

5 students like to play both games.

GOOD LUCK !!