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JEE Main202311 Apr 2023Morning ShiftMathematicsSets and RelationsActual

An organization awarded 48 medals in event A ' ' , 25 in event B ' ' and 18 in event C ' ' . If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

Options

  1. A15
  2. B21
  3. C10
  4. D9

Correct answer

B. 21

Step-by-step solution

Let A ,   B and C denote the set of men who received medals in even A , event B and event C respectively. Then, n A = 48 ,   n B = 25 ,   n C = 18 , n A ∪ B ∪ C = 60 and n A ∩ B ∩ C = 5 , Now we know that, n A ∪ B ∪ C = n A + n B + n C - n A ∩ B - n A ∩ C - n B ∩ C + n A ∩ B ∩ C ⇒ 60 = 48 + 25 + 18 - n ( A ∩ B ) - n ( A ∩ C ) - n ( B ∩ C ) + 5 ⇒ n ( A ∩ B ) + n ( A ∩ C ) + n ( A ∩ C ) = 4

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