Bonsoir,
[tex]\left(\begin{array}{c}n\\ 7\end{array}\right)=\dfrac{n!}{7!(n-7)!} \\\\\\\left(\begin{array}{c}n\\ 3\end{array}\right)=\dfrac{n!}{3!(n-3)!} \\\\\\\dfrac{3!}{7!}=\dfrac{(n-7)!}{(n-3)!} \\\\\\(n-3)(n-4)(n-5)(n-6)=7*6*5*4\\\\\\n-6=4\Longleftrightarrow n=10\\n-5=5\Longleftrightarrow n=10\\n-4=6\Longleftrightarrow n=10\\n-3=7\Longleftrightarrow n=10\\[/tex]
Donc n=10
