Question

Out of 120 farmers 93 farmers grows vegetables, 63 grows flowers,45 grows sugarcane,45 grows vegetables flowers, 24 grows flowers sugarcane, 27 grows vegetables sugarcane find how many farmers grows all the three?

Answer 1

We know that:-

$n\left(A+B+C\right)=n\left(A\right)+n\left(B\right)+n\left(C\right)-n\left(A\cap B\right)-n\left(B\cap C\right)-n\left(C\cap A\right)+n\left(A\cap B\cap C\right)$

$\Rightarrow 120=93+63+45-45-24-27+n\left(A\cap B\cap C\right)$

$\Rightarrow n\left(A\cap B\cap C\right)=15$

Thus, 15 farmers grow all 3.