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?
According to the question,
Total number of students = 60
Students who play cricket = 25
Students who play tennis = 20
Students who play both the games = 10
To find: number of students who play neither
Let the total number of students = S
Let the number of students who play cricket = C
Let the number of students who play tennis = T
n(S) = 60, n(C) = 25, n(T) = 20, n(C ∩ T) = 10
So, Number of students who play either of them,
n(C ∪ T) = n(C) + n(T) – n(C ∩ T)
= 25 + 20 – 10
= 35
Hence, Number of student who play neither = Total – n(C ∪ T)
= 60 – 35
= 25
Therefore, there are 25 students who play neither cricket nor tennis.