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1.Set Theory
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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
$15$
(JEE MAIN-2023)
Solution
$| A |=48$
$| B |=25$
$| C |=18$
$| A \cup B \cup C |=60 \quad[\text { Total }]$
$| A \cap B \cap C |=5$
$|A \cup B \cup C|=\sum|A|-\sum|A \cap B|+|A \cap B \cap C|$
$\Rightarrow \sum|A \cap B|=48+25+18+5-60$
$\quad=36$
No. of men who received exactly 2 medals
$=\sum|A \cap B|-3|A \cap B \cap C|$
$=36-15$
$=21$
Standard 11
Mathematics
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