Question

In a school, all the students play either Foot ball or Volley ball or both. 300 students play Foot ball, 270 students play Volley ball and 120 students play both games. Find
(i) The number of students who play Foot ball only
(ii) The number of students who play Volley ball only
(iii) The total number of students in the school

Answer 1

Let, the number of students who play Football$=n\left(A\right)=300$

No of students who play Volley ball$=n\left(B\right)=270$

No of students who play both games $=n(A\cap B)=120$

(i)No of students who play Football only$=n(A-B)=n\left(A\right)-n(A\cap B)$

$=n(A-B)=n\left(A\right)-n(A\cap B)=300-120=180$

(ii) No of students who play Volley Ball only $=n(B-A)=n\left(B\right)-n(A\cap B)=270-120=150$

(iii) Total no of students in School $=n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$=270+300-120=450$