Question

A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to total of 58 men and only three men got medals in all the three sports. Number of person who get medals in exactly two of the three sports is

• A. 15
• B. 9
• C. 18
• D. 12

Answer 1

The correct option is C 18

Let F, B and C be the sets of men who got medals in football, basketball and cricket.
These medals went to total 58 men i.e. n(F∪B∪C) = 58
Number of persons who got medals all three sports = n(F∩B∩C) = 3

n(F) = 38, n(B) = 15, n(C) = 20
n(F∪B∪C) = n(F) + n(B) + n(C) – n(F∩B) – n(B∩C) – n(C∩F) + n(F∩B∩C)
⇒ 58 = 38 + 15 + 20 – n(F∩B) – n(B∩C) – n(C∩F) + 3
⇒ n(F∩B) + n(B∩C) + n(C∩F)
= 76 – 58 = 18

So, option c is correct.