A college awarded 38 medals in football 15 in basketball 20 cricket if these medals went to a picture of 58 men and men got medals in all the three sports. Find number of medals received by the men exactly in two of the three sports.
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n(FUBUC) = n(F) + n(B) + n(C) - n(BnC) - n(FnB) - n(FnC) + n(FnBnC)
58 = 38 + 15 + 20 - [n(BnC) + n(FnB) + n(FnC)] + 3
18 = [n(BnC) + n(FnB) + n(FnC)]
Number of men who received medals in exactly two of the three sports
=n(FnBnC') + n(FnB'nC) + n(F'nBnC)
=n(BnC) + n(FnB) + n(FnC) - 3n(FnBnC)
=9 {Since n(FnBnC') = n(FnB) - n(FnBnC)}
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Answer:
n(FUBUC) = n(F) + n(B) + n(C) - n(BnC) - n(FnB) - n(FnC) + n(FnBnC) 58 = 38 + 15 + 20 - [n(BnC) + n(FnB) + n(FnC)] + 3 18 = [n(BnC) + n(FnB) + n(FnC)] Number of men who received medals in exactly two of the three sports =n(FnBnC') + n(FnB'nC) + n(F'nBnC) =n(BnC) + n(FnB) + n(FnC) - 3n(FnBnC) =9 {Since n(FnBnC') = n(FnB) - n(FnBnC)}
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