Question

rezolvati ecuatia. combinatorica. va rof urgent​

Answer 1

$\it \Big A_n^7-\Big A_n^6=8\Big A_n^5 \Rightarrow \dfrac{n!}{(n-7)!}-\dfrac{n!}{(n-6)!}=8\cdot\dfrac{n!}{(n-5)!} \Big |_{ \cdot\dfrac{(n-7)!}{n!}} \Rightarrow\\ \\ \\ \Rightarrow 1-\dfrac{1}{n-6}=8\cdot\dfrac{1}{(n-5)(n-6)}\Big |_{\cdot(n-6)} \Rightarrow n-6-1=\dfrac{8}{n-5} \Rightarrow\\ \\ \\ n-7=\dfrac{8}{n-5}|_{\cdot(n-5)} \Rightarrow (n-7)(n-5)=8 =2\cdot4 \Rightarrow n-7=2\Rightarrow n=9$