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  • In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Then, the number of students who play neither is (a) 0 (b) 25 (c) 35 (d) 45

 In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Then, the number of students who play neither is
(a) 0 (b) 25 (c) 35 (d) 45

Answers (1)

 The answer is the option (b).

Let C be the set of students who play cricket and T the set of students who play tennis.
Total number of students = 60 ⇒n(U)=60
Number of students who play cricket = 25 \Rightarrow n(C)=25
Number of students who play tennis = 20 \Rightarrow n(T)=20
Number of students who play both the games = 10 \Rightarrow n(C\cap T) = 10
Number of students who play any one game= n (C \cup T ) =n(C ) +n(T) - nC\cap T = 25+20=10 =35
Number of students who play neither = n(U) - n(C \cup T) = 60-35 = 25

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