Question

In a school of 200 students, 120 play foot ball, 70 play cricket and 60 play both, then find the number of students play neither foot ball or nor cricket.

Answer 1

We have,

$Totalstudent=n\left(U\right)=200$

Football play $n\left(F\right)=120$

Cricket play $n\left(C\right)=70$

Both played $n(F\cap C)=60$

Then,

Neither football play $n\left(F^{\prime }\right)=?$

Nor cricket play $n\left(C^{\prime }\right)=?$

Then,

We know that,

$n(C\cup F)=n\left(C\right)+n\left(F\right)-n(C\cap F)$

$n(C\cup F)=120+70-60$

$n(C\cup F)=130$

$Sonumberofstudentsnotplayingeitheris200-130=70$

Hence, this is the answer.