there are 240 students in a class 9 of a school; 130 play cricket,100 play football ,75 play volleyball - Maths -

Question

there are 240 students in a class 9 of a school; 130 play
cricket,100 play football ,75 play volleyball , 30 of these pla
cricket , and football ,25 play cricket and volleyball ,15 play
football and volleyball also each student plays atleast one of the
three games find how many students play all the three games answer
fast

Lovina Kansal · Accepted Answer

Dear student
Let C,F and V denote the set of students who play cricket,football and vollyball respectively,Then , we haven(U)=240n(C)=130n(F)=100n(V)=75nC∩F=30n(C∩V)=25n(F∩V)=15n(C∪F∪V)=240So, students whos play all three games=nC∩F∩V=n(C∪F∪V)-nC-nF-nV+nC∩F+n(C∩V)+n(F∩V)=240-130-100-75+30+25+15=5
Regards