Question

in a class of 106 students,each student studies at least one of the three subjects maths,physics and chemistry,48 of them study maths,51studies physics and 53 studies chemistry.16 studies maths and physics,17 study maths and chemistry and 18 study physics and chemistry​

Answer 1

Numbers of students who are studying all three subjects is $5$

Explanation:

Given that,

Total number of students $M \cup P \cup C = 106$

Only mathematics students $M = 48$

Only physics students $P = 51$

Only chemistry students  $C = 53$

Mathematics and physic students $( M \cap P) = 16$

Mathematics and chemistry students $(M\cap C) = 17$

Physics and chemistry students $(P\cap C) = 18$

As we know that, $M \cup P \cup C = M + P + C - ( M \cap P) - (M\cap C) - (P\cap C) + ( M \cap P \cap C)$

$106 = 48 + 51 + 53 - 16 - 17 - 18 + ( M \cap P \cap C)$

$( M \cap P \cap C) = 106 - 101$

$( M \cap P \cap C) = 5$

Numbers of students who are studying all three subjects is $5$