Math, asked by Asadshahid17, 11 months ago

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?​

Answers

Answered by amitnrw
1

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

Similar questions