Out of 1020 boys in a school , 406 play cricket, 324 play hockey and 250 play football,80 boys play - Maths - Sets

Question

Out of 1020 boys in a school , 406 play cricket, 324 play
hockey and 250 play football,80 boys play cricket and hockey, 64
play hockey and football ,92 play football and cricket while 30
play all the three games How many boys play none of the games?

Nishima Pasricha · Accepted Answer

Let C, H, F be the set of boys who play cricket, hockey, football repectively
Then, nC=406, nH=324, nF=250, nC∩H=80, nH∩F=64, nF∩C=92nC∩H∩F=30Number of people who play atleast one of the games=nC∪H∪F=nC+nH+nF-nC∩H-nH∩F-nF∩C+nC∩H∩F=406+324+250-80-64-92+30=774∴Number of boys who play none of the games=1020-774=246

Out of 1020 boys in a school , 406 play cricket, 324 play hockey and 250 play football,80 boys play cricket and hockey, 64 play hockey and football ,92 play football and cricket while 30 play all the three games. How many boys play none of the games?