CBSE Class 11-science Answered
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 | 21 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 | 21 Jul, 2012, 08:48: PM
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