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 Jul, 2012, 11:40: AM

Expert 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)}

Answered by  | 21st Jul, 2012, 08:48: PM

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