In a group 315 players play at least one sport.100 play cricket, 150 play hockey and 200 play football. If 75 of them play exactly two sports how many play all three sports?
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Answer:
play all three sports = 30
Step-by-step explanation:
In a group 315 players play at least one sport.100 play cricket, 150 play hockey and 200 play football. If 75 of them play exactly two sports how many play all three sports?
Total = 315
Play none N = 0
Cricket = C = 100
Hockey = H = 150
FootBall = F = 200
Total = C + H + F - C∩H - C∩F - F∩H + C∩F∩H + N
=> 315 = 100 + 150 + 200 - (C∩H + C∩F +F∩H) + C∩F∩H + 0
=> -135 = - (C∩H + C∩F +F∩H) + C∩F∩H
Exactly Both Games
(C∩H - C∩F∩H) + (C∩F - C∩F∩H) + (F∩H - C∩F∩H) = 75
=> C∩H + C∩F +F∩H = 75 + 3C∩F∩H
-135 = -(75 + 3C∩F∩H) + C∩F∩H
=> -60 = -2C∩F∩H
=> C∩F∩H = 30
play all three sports = 30
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