Mathematics Question from JEE Main 2024 · 30 January, Shift 1

A group of $40$ students appeared in an examination of $3$ subjects — Mathematics, Physics and Chemistry. It was found that all students passed in at least one of the subjects, $20$ students passed in Mathematics, $25$ students passed in Physics and $16$ students passed in Chemistry; at most $11$ students passed in both Mathematics and Physics, at most $15$ students passed in both Physics and Chemistry, and at most $15$ students passed in both Mathematics and Chemistry. The maximum number of students who passed in all three subjects is _____.