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# A college awarded 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?

Asked by R.K. Kumar 21st July 2012, 11:40 AM
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)}
Answered by Expert 21st July 2012, 8:48 PM
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