If N is a product of factorial of four consecutive positive integers then which of the following is/are correct

(Q). If N is a product of factorial of four consecutive positive integers then which of the following is/are correct about N.

(i) if N is a three digit number then there exists two such value of N. ➡ ✖
(ii) if N is a Five digit number then there exists only one such value of N. ➡ ✔ 
(iii) N may be a four digit number.  ➡✖

Solution:- 

if N = 1!.2!.3!.4! = 288 
   N = 2!.3!.4!.5! = 34560 
   N = 3!.4!.5!.6! = 12441600
   N = 4!.5!.6!.7! = 10450944000