\\\\(\ extbf{Step – 1: Formulating the information to use Inclusion-Exclusion Rule.}\\\\) \\\\(\ ext{Let number of men who have got medals in football, basketball, and cricket be represented as}\\\\) \\\\(n(F),n(B)\\\\) and \\\\(n(C)\\\\). \\\\(\ ext{Therefore the number of men who won in all the three sports will be}\\\\) \\\\(n(F \\cap B \\cap C)\\\\) \\\\(\ ext{and the number of people who got medals in two of the three sports is}\\\\) \\\\(n(F \\cap B) + n(B \\cap C) + n(C \\cap F)\\\\) \\\\(\ ext{and the total number of men is represented as}\\\\) \\\\(n(F \\cup B \\cup C)\\\\). \\\\(\ ext{From the given data we have:}\\\\) \\\\(n(F) = 38\\\\) \\\\(n(B) = 15\\\\) \\\\(n(C) = 20\\\\) \\\\(n(F \\cup B \\cup C) = 58\\\\) \\\\(n(F \\cap B \\cap C) = 3\\\\)\\\\(\ extbf{Step – 2: Apply the Inclusion-Exclusion Rule}\\\\). \\\\(\ ext{Using the Inclusion-Exclusion Rule we get:}\\\\) \\\\(n(F \\cup B \\cup C) = n(F) + n(B) + n(C) - n(F \\cap B) - n(B \\cap C) - n(C \\cap F) + n(F \\cap B \\cap C)\\\\) \\\\(\\Rightarrow 58 = 38 + 15 + 20 - n(F \\cap B) - n(B \\cap C) - n(C \\cap F) + 3 \\\\) \\\\(\\Rightarrow n(F \\cap B) + n(B \\cap C) + n(C \\cap F) = 38 + 15 + 20 + 3 - 58 \\\\) \\\\(\\Rightarrow n(F \\cap B) + n(B \\cap C) + n(C \\cap F) = 18 \\\\) \\\\(\ herefore\ ext{ the number of students who have received medals in exactly two of the three sports is}\\\\) \\\\({= n(F \\cap B) + n(B \\cap C) + n(C \\cap F) - 3 \ imes n(F \\cap B \\cap C) }\\\\) \\\\({= 18 - 3 \ imes 3 }\\\\) \\\\({= 18 - 9}\\\\) \\\\({= 9}\\\\)\\\\(\ extbf{Hence, the number of students who have received medals in exactly two of the three sports is 9}\\\\)