Solve for n:

Question

(n-2)!/(n-3)!=15
and
(n-2)!/(n-1)=12

Answer 1

I'll solve the first one, and the second one can be solved similarly.

(n-2)!/(n-3)!
=(n-2)(n-3)!/(n-3!)
=n-2
therefore n-2=15 => n=17
Check:
(17-2)!/(17-3)!=15!/14!=15*14*...*1/(14*13*..*1)
=15 checked ok.