Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game is:
Answer: D
We use the formula for the union of three sets:
n(C ∪ H ∪ B) = n(C) + n(H) + n(B) - n(C ∩ H) - n(H ∩ B) - n(C ∩ B) + n(C ∩ H ∩ B)
n(C ∪ H ∪ B) = 224 + 240 + 336 - 40 - 64 - 80 + 24
n(C ∪ H ∪ B) = 800 - 184 + 24 = 640.
This is the number of boys who played at least one game.
Number of boys who did not play any game = Total boys - n(C ∪ H ∪ B) = 800 - 640 = 160.