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Question
In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Find the number of students who play neither?
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Solution
Given: Total number of students are 60
Students who play cricket and tennis are 25 and 20 respectively
Students who play both the games are 10
To find: Number of students who play neither
Let S be the total number of students
C and T be the number of students who play cricket and tennis respectively
n(S) = 60
n(C) = 25
n(T) = 20
n(C ∩ T) = 10
Number of students who play either of them = n(C ∪ T)
= n(C) + n(T) – n(C ∩ T)
= 25 + 20 – 10
= 35
Number of student who play neither
= Total – n(C ∪ T)
= 60 – 35
= 25
Hence, there are 25 students who play neither cricket nor tennis.
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