#  don't work with TOC?

If i write this line of code

\subsection{Ranger $$n$$ boules distinguables dans $$M$$ boîtes}


I obtain an error over the second \)

(./Probabilité.toc

./Probabilité.toc:8: LaTeX Error: Bad math environment delimiter.


while if I write

\subsection{Ranger $n$ boules distinguables dans $M$ boîtes}


everything is ok. Why? I'm doing something wrong?

-

$$ and $$ are not robust, you need to \protect them. Or load package fixltx2e that makes them robust.
(Update:) Package fixltx2e defines the command \MakeRobust that redefines a macro in the same way, as the macro would has been defined by using \DeclareRobustCommand in the first place.
"Robust" means, that the macro can be used inside moving arguments (entries for the table of contents, header lines, …) without breaking and the need to add \protect in front of them.