In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games.

the number of students who play neither

Answers is 25

Let C be the set of students who play cricket and T be the set of students who play tennis.

n(U) = 60, n(C) = 25, n(T) = 20, and n(C ∩ T) = 10

n(C ∪ T) = n(C) + n(T) – n(C n T) = 25 + 20 – 10 = 35

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.

B. 25

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.