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

Question

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

Tardigrade Admin · Accepted Answer

Let student play cricket =C Student play tennis =T and total number of students =S ∴ n(S) =60, n(C)=25, n(T)=20 and n(C ∩ T) =10 Now, n(C ∪ T) =n(C)+n(T)-n(C ∩ T) =25+20-10=35 ∴ The number of students who play neither game =n(C ∩ T)'=n(S)-n(C ∪ T) =60-35=25

Q. 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

$0$

$25$

$35$

$45$

Q. 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

0

25

35

45

Let student play cricket =C Student play tennis =T and total number of students =S ∴n(S)=60,n(C)=25,n(T)=20 and n(C∩T)=10 Now, n(C∪T)=n(C)+n(T)−n(C∩T) =25+20−10=35 ∴ The number of students who play neither game =n(C∩T)′=n(S)−n(C∪T) =60−35=25

Q. 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

$0$

$25$

$35$

$45$