In a class of 30 students, 18 students play cricket, 15 students play football and 12 play both the games. How many students in the class don't play either of the games?
In a class of 30 students, 18 students play cricket, 15 students play football and 12 play both the games. How many students in the class don't play either of the games?
The correct option is A 9
The Venn diagram of the above problem will look like
In the above diagram, the square represents universal set i.e., number of students in the class.
The circles F and C represent students playing football and cricket.
The region which is outside those circles is the number of students not playing either of games.
The total number of students in the circle i.e., students playing either football or cricket = n (F) + n (C) - n (F ∩ C)
= 15 + 18 - 12 = 21
We will subtract this from the total number of students to get the students who do not play anything.
Therefore, Number of students who do not play any game = 30 - 21 = 9
The Venn diagram of the above problem will look like
In the above diagram, the square represents universal set i.e., number of students in the class.
The circles F and C represent students playing football and cricket.
The region which is outside those circles is the number of students not playing either of games.
The total number of students in the circle i.e., students playing either football or cricket = n (F) + n (C) - n (F ∩ C)
= 15 + 18 - 12 = 21
We will subtract this from the total number of students to get the students who do not play anything.
Therefore, Number of students who do not play any game = 30 - 21 = 9
