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QJEEM24Maedc5: JEE Main 2024 Mathematics - Class 12 JEEM24Maedc5 Solution: A group of 40 students appeared in an examination of 3 subjects …

A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics and Chemistry. It was found that all students passed in atleast one of the subjects, 20 students passed in Mathematics, 25 students passed in Physics, 16 students passed in Chemistry, atmost 11 students passed in both Mathematics and Physics, atmost 15 students passed in both Physics and Chemistry, atmost 15 students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is _________.

Step-by-Step Verified Solution

amp;n(M)=20amp;n(P)=25amp;n(C)=16amp;n(M∩P)=11amp;n(P∩C)=15amp;n(M∩C)=15\begin{aligned} & n(M)=20 \\\\ & n(P)=25 \\\\ & n(C)=16 \\\\ & n(M \cap P)=11 \\\\ & n(P \cap C)=15 \\\\ & n(M \cap C)=15\end{aligned}
JEE Main 2024 (Online) 30th January Morning Shift Mathematics - Probability Question 27 English Explanation
amp;n(C∪P∪M)≤n(U)=40.amp;n(C)+n(P)+n(M)−n(C∩M)−n(P∩M)−n(C∩amp;P)+n(C∩P∩M)≤40amp;20+25+16−11−15−15+x≤40amp;x≤20\begin{aligned}& n(C \cup P \cup M) \leq n(U)=40 . \\\\& n(C)+n(P)+n(M)-n(C \cap M)-n(P \cap M)-n(C \cap \\\\& P)+n(C \cap P \cap M) \leq 40 \\\\& 20+25+16-11-15-15+x \leq 40 \\\\& x \leq 20\end{aligned}

But 11−x≥011-x \geq 0 and 15−x≥015-x \geq 0

⇒x≥11\Rightarrow x \geq 11

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