A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics and…

Question

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...

Answer: 10

Accepted Answer

$\begin{gathered} n(M)=20 \ n(P)=25 \ n(C)=16 \ n(M\cap P)=11 \ n(P\cap C)=15 \ n(M\cap C)=15 \end{gathered}$

$\begin{gathered} n(C\cup P\cup M)\le n(U)=40. \ n(C)+n(P)+n(M)-n(C\cap M)-n(P\cap M)-n(C\cap \ P)+n(C\cap P\cap M)\le 40 \ 20+25+16-11-15-15+x\le 40 \ x\le 20 \end{gathered}$

But $11-x\ge 0$ and $15-x\ge 0$

$\Rightarrow x\ge 11$

Solutions · 1