Question

Out of $100$ students $15$ passed in English $12$ passed in Mathematics, $8$ Science, $4$ in English and Science in all the three. Find how many passed in more than one subject only?

Answer 1

Given$n(\cup )=100$

$n\left(E\right)=15,$

$n\left(M\right)=12,$

$n\left(S\right)=8$

$n\left(E\cap M\right)=6,n\left(M\cap S\right)=7,$

$n\left(E\cap S\right)....4,andn\left(E\cap M\cap S\right)=4$

$a=n\left(E\cap M\cap S\right)=4$

$a+d=n\left(M\cap S\right)=7$

$\therefore d=3$

$a+b=n\left(M\cap E\right)=6$

$\therefore b=2$

$a+c=n\left(S\cap E\right)=4$

$\therefore c=0$

$a+b+d+e=n\left(M\right)=12$

$\therefore 4+2+3+e=12$

$\therefore e=3$

$a+b+c+g=15$

$\therefore 4+2+0+g=n\left(E\right)=15$

$\therefore g=9$

$a+c+d+f=n\left(S\right)=8$

$\therefore 4+0+3+f=8$

$\therefore f=1$

The number of students pass in more than one subject $=a+b+c+d=4+2+0+3=9$