JEE Mains · Maths · STD 11 - 1. set theory
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?
- A \(10\)
- B \(9\)
- C \(21\)
- D \(15\)
Answer & Solution
Correct Answer
(C) \(21\)
Step-by-step Solution
Detailed explanation
\(| A |=48\) \(| B |=25\) \(| C |=18\) \(| A \cup B \cup C |=60 \quad[\text { Total }]\) \(| A \cap B \cap C |=5\) \(|A \cup B \cup C|=\sum|A|-\sum|A \cap B|+|A \cap B \cap C|\) \(\Rightarrow \sum|A \cap B|=48+25+18+5-60\) \(\quad=36\) No. of men who received exactly 2 medals…
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