In a school having 100 students. 50 members play chess, 30 member play caroms. 30 member will play neither caroms nor chess, then how many play Both chess and caroms

Total number of students in a school $n\left(\mu \right)=100$

Number of students play chess $n\left(A\right)=50$

Number of students play caroms $n\left(B\right)=30$

Number of  students play neither chess nor Caroms  $n\left(\left(A\cup B^{-}\right)\right)=30$  

Number of  Pupil Play either chess (or) caroms $n\left(A\cup B\right)=n\left(\mu \right)-n{\left(A\cup B\right)}^c$ $=100-30=70$

Number of Pupil play Both chess and caroms

$n\left(A\cap B\right)=?$

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

$=50+30-70=10$