Question

In a class of 150 students, 65 play football, 50 play hockey, 75 play cricket, 35 play hockey and cricket, 20 play football and cricket, 42 play football and hockey and 8 play all the three games. Find the number of students who do not play any of these three games.

Answer 1

Answer: 49 students do not play any of the three games.

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Step-by-step explanation:  Let us consider the following sets-

F=the set of students who play football,

H=the set of students who play hockey

and

C=the set of students who play cricket.

Therefore, according to the given information, we have

$n(F)$=the number of students who play football=$65$,

$n(H)=50$, $n(C)=75$, $n(F\cap H)= 42$, $n(H\cap C)=35$, $n(F\cap H)=20$ and

$n(H\cap F\cap C)=8.$

So, from set theory, we have

$n(F\cup H\cup C)=n(F)+n(H)+n(C)-n(F\cap H)-n(H\cap C)-n(C\cap F)+n(F\cap H\cap C)\\\\ \Rightarrow n(F\cup H\cup C)= 65+50+75-42-35-20+8=101$

So, the number of students who play atleast one of football, hockey or cricket is 101. Since there are total 150 students in the class, so the number of students who do not play any one of the games=150-101=49.

Thus, the answer is 49.