A college warded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports?

Options

A. 18
B. 15
C. 9
D. 6

Answer

C

Explanation

Let F,B and C denote the sets of students who receiced medals in football ,Basketball and cricket recpectively , then , we have
`n(F)=37 ,n(B) =15,n( C ) =20, `
` n(FcupBcup C)=58 and n(F capB cap C) =3`
Now,
`n(Fcup bcup C)=n(F)+n( C) -n(FcapB)-n(BcapC)-n(C cap F)+n(fcapBcapC)`
`implies 58=38+15+20 -{n(Fcap B)+n(B capC)+n( C cap F)|+3`
`implies n(F cap B)+(Bcap C)+n(C capF)=18`
hence the number of students who medals in exactly two of the sports
`=n(F cap B)+n(B capC)+n(C capF)-3n(FcapBcapC)`
`=18-3xx3=9.`