Explications étape par étape:
We can simplify the given equation step by step as follows:
n!/(n-8)! = n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)(n-7)(n-8)/(n-8)!
n!/(n-8)! = n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)(n-7)
n!/(n-5) = n(n-1)(n-2)(n-3)(n-4)(n-5)
Therefore, the initial equation can be written as:
n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)(n-7) / [n(n-1)(n-2)(n-3)(n-4)(n-5)] = 360(n-6)!
(n-6)(n-7) = 360(n-6)!
n-6 = 360
n = 366
Therefore, the solution to the equation is n = 366.
