Question

out of 800 boys in a school, 224 played cricket, 240 play hockey and 336 played
basket ball. Out of total 64 played both basket ball and hockey,80 played cricket and basketball and40 played cricket and hockey, 24 played all the three games. Find No of
boys who did not play any game.​

Answer 1

Answer:

Total no. of boys n(X)=800

Let n(C)=boys who played cricket

n(H)=boys who played hockey

n(B)=boys who played basket ball

∴n(C)=224,n(H)=240,n(B)=336,n(B∩H)=64,n(C∩B)=80,n(C∩H)=40,n(C∩H∩B)=24

∴n(C∪H∪B)=n(C)+n(H)+n(B)−n(B∩H)−n(C∩B)−n(B∩H)+n(C∩H∩B)

⇒224+240+336−64−80−40+24=640

The number of boys who did not play any game=n(X)−n(C∪H∪B)

⇒800−640=160