Question

out of 800 Boys in a school,224 played cricket, 240 played hockey and 336 played basket Ball. of the total 64 played both basket Ball and hockey, 80 played cricket and basket Ball and 40 played cricket and hockey ,24 played all the games the no. of Boys Who did not play any games? ​

Answer 1

Step-by-step explanation:

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

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