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Home » 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?
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?
CBSE | Class 11 | Maths | NCERT Exemplar | Sets
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?

Solution:

As per the question,

60 = Total number of students

25 = Students who play cricket

20 = Students who play tennis

10 = Students who play both the games

We need to find: the number of students who play neither

Let S = the total number of students

Let C = the number of students who play cricket

Let T = the number of students who play tennis

\mathrm{n}(\mathrm{S})=60, \mathrm{n}(\mathrm{C})=25, \mathrm{n}(\mathrm{T})=20, \mathrm{n}(\mathrm{C} \cap \mathrm{T})=10

So, the no. of students who play either of them,

n(C \cup T)=n(C)+n(T)-n(C \cap T)

=25+20-10

=35

Therefore, No. of student who play neither = Total -n(C \cup T) =60- 35 =25

As a result, number of students who play neither cricket nor tennis is 25.

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