In a group of 80 people, 55 people like Table Tennis and 23 people like both Table tennis and Carrom. Everyone in the group likes at least one of the two games. How many people like only Carrom?

In a group of 80 people, 55 people like Table Tennis and 23 people like both Table tennis and Carrom. Everyone in the group likes at least one of the two games. How many people like only Carrom? Correct Answer 25

Given:

In a group of 80 people, 55 people like Table Tennis and 23 people like both cricket and Carrom

 Everyone in the group like at least one of the two games

Formula used:

n(C U T) = n(C) + n(T) - n(C ∩ T) 

Explanation:

Let C and T denote people who like Carrom and Table Tennis respectively

Total number of people = Number of people who like Table Tennis or Carrom

⇒ n(C U T) = 80

Number of people who like Table Tennis = n(T) = 55

Number of people who like both Table Tennis and Carrom = n(C ∩ T) = 23

Now,

n(C U T) = n(C) + n(T) - n(C ∩ T) 

⇒ n(C) = n(C U T) + n(C ∩ T) - n(T)

⇒ n(C) = 80 + 23 - 55 = 48

∴ Number of people like only Carrom = 48 - 23 = 25