1.Set Theory
hard

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

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.