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Question

In a class of 30 students, 18 students play cricket, 15 students play football 12 play both the games. How many students in the class don't play both the games?


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Solution

The Venn diagram of the above problem will look like

We want to find how many students don't play any game or according to the Venn diagram, how many students lie outside the circle, but inside the square. If we can find the number of students in the two circles combined, we can find the number of students who does not play any game. The total number of students is 30.

We know how many students play football, cricket and both. We will add the students who play football and cricket. We have to subtract the students who play both from this because the students who play both are included twice; once in the students who play football and once in the students who play cricket.

The total number of students in the circle = 15+18-12 = 21

We will subtract this from the total number of students to get the students who does not play anything

Number of students who does not play any game = 30-21 = 9

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