There are $100$ students in a class. In a test, $50$ of them failed in mathematics, $45$ failed in physics and $40$ failed in chemistry. $32$ failed in exactly two of these three subjects.Only one student passed in all the three subjects.The number of students failing in all three subjects is
As only one student has passed in all three subjects so $99$ students have failed in at least one subject. Denoting fail in mathematics as $M$, physics as $P$, chemistry as $C$. $MP$ denotes fail in math and phy. similarly $PC$ and $MC$. $MPC$ denote fail in all three subjects.
Number of students failed in $M$ OR $P$ OR $C$ = $M+P+C-MP-PC-MC+MPC$
Given that $32$ students failed exactly in two of these subjects. so $MP+PC+MC=32$.
Whats wrong here?
Help appreciated :)