[tex]\displaystyle\bf\\A_n^7=336 A_{n-3}^4\\\\\underbrace{n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)}_{7~factori}=\\\\=336\underbrace{(n-3)(n-4)(n-5)(n-6)}_{4~factori}~~~\Big|~: (n-3)(n-4)(n-5)(n-6)\\\\\\n(n-1)(n-2)=336\\\\n(n-1)(n-2)~este~un~produs~de~3~numere~consecutive.\\\\Il~scriem~pe~336~ca~produs~de~3~numere~consecutive.\\\\336=2^4\times3\times7\\\\336=2^3\times(2\times3)\times7\\\\n(n-1)(n-2)=336=8\times7\times6\\\\\implies~~\boxed{\bf n=8}[/tex]
