A college awarded 38 medals in football, 15 in basket ball 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 sprots is
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a
9
b
18
c
27
d
3
answer is A.
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Detailed Solution
Let F, B, C denote the set of men who received medals in football, basketball and cricket respectively.nF∩B+nB∩C+nC∩F=18⇒a+d+b+d+c+d=18∵d=nF∩B∩C=3a+b+c=9