Question

Out of 880 boys in a school, 224 played cricket, 240 played hockey & 336 played basketball. Of the total 64 played both basketball & hockey; 80 played cricket & basket ball & 40 played cricket & hockey. 24 boys played all the three games. How many boys did not play any game, & how many played only one 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