Question

$\frac{(n+4)!}{n!}=360$

Answer 1

(n+4)!/n!=360
n!(n+1)(n+2)(n+3)(n+4)/n!=360
(n+1)(n+2)(n+3)(n+4)=360
n^4+10n^3+35n^2+50n+24-360=0
(n-2)(n+7)(n^2+5n+24)=0
n=2
n=-7