Aranjamente de n elemente luate câte 6 + aranjamente de n elemente luate câte 5 supra aranjamente de n elemente luate câte 4

Sper ca te am ajutat

[tex]\dfrac{A^{6}_n+A^{5}_n}{A^{4}_n}= \dfrac{ \frac{n!}{(n-6)!}+\frac{n!}{(n-5)!}}{\frac{n!}{(n-4)!}}= \frac{(n-4)!}{(n-6)!}+\frac{(n-4)!}{(n-5)!}=\frac{(n-6)!\cdot(n-5)(n-4)}{(n-6)!}+\\ \frac{(n-5)!\cdot (n-4)}{(n-5)!}=(n-5)(n-4)+(n-4)=(n-4)(n-5+1)=\\ =\boxed{(n-4)^2}[/tex]