A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics and Chemistry. It was found that all students passed in…

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