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At Mallard High School there are three intramural sports leagues: football, basketball, and baseball. There are 427 students participating in these sports: 128 play on football teams, 291 play on basketball teams, and 318 play on baseball teams. If exactly 36 students participate in all three of the sports, how many students participate in exactly two of the sports?

 

So I tried to start by using intersections and unions to see if I could get anywhere. I also have a Venn diagram that I drew. So I have that \(A=128, B=291, \) and \(C=318.\)

 

I also have that \(A\cap B\cap C=36, A\cup B\cup C=A+B+C-A\cap B-A\cap C-B\cap C+A\cap B\cap C=427.\) However, I can't find what the intersection of any of the sections should be, so I would really appreciate any help with this problem. 

 Apr 4, 2020
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When I draw Venn I come up with 238 must play two sports   ....

 Apr 4, 2020
edited by ElectricPavlov  Apr 4, 2020

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