Question

Análise Combinatória Fatorial​

Answer 1

$a) \dfrac{(n+1)!}{(n-1)!} = 12 \\\\\dfrac{(n+1)n(n-1)!}{(n-1)!} = 12\\\\\ (n+1)n = 12\\\\ \boxed{n = 3}\\\\\\b) \dfrac{(n+10)!}{(n+8)!} = 30\\\\\dfrac{(n+10)(n+9)(n+8)!}{(n+8)!} = 30\\(n+10)(n+9) = 30\\n^2 + 9n + 10n + 90 = 30\\n^2 + 19n + 60 = 0\\\\n' = -4\\n'' = -15\\\\\boxed{n = - 4}\\\\\mathsf{Pois,}\\\\(n+10)! \rightarrow (10-15)! \rightarrow -5!\\\\\mathsf{Nao\ existe\ fatorial\ de\ numero\ negativo.}\\\\\\c) \boxed{n = 1\ ou\ n = 0}$

Abraços!