Question

If in a class there are $200$ students in which $120$ take Mathematics, $90$ take Physics, $60$ take Chemistry, $50$ take Mathematics & Physics, $50$ take Mathematics & Chemistry, $43$ take Physics & Chemistry and $38$ take Mathematics, Physics & Chemistry, then the number of students who have taken exactly one subject is

• A. $42$
• B. $56$
• C. $270$
• D. $98$

Answer 1

Answer: (D)

Let, $M \rightarrow $ Mathematics, $P \rightarrow $ Physics, $C \rightarrow $ Chemistry
Given that total students $=200$
$n\left(M\right)=120,$ $n\left(P\right)=90,n\left(C\right)=60$
$n\left(M \cap P\right)=50,$ $n\left(M \cap C\right)=50,n\left(P \cap C\right)=43$
$n\left(M \cap P \cap C\right)=38$
Required number of students taking exactly one subject is
$n\left(M\right)+n\left(P\right)+n\left(C\right)-2n\left(M \cap P\right)-2n\left(P \cap C\right)-2n\left(M \cap C\right)+3n\left(M \cap P \cap C\right)$
$=120+90+60-2\left(50\right)-2\left(50\right)-2\left(43\right)+3\left(38\right)$
$=98$