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. $45$

Answer 1

Answer: (B)

$25$

Answer 2

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