Modular Arithmetic: prove (7n)! / (7^(n-1) * n! ), for some int. n, equals mod 7

[DanCo128]

I have been trying to solve this problem about modular arithmetic now for a long time... I'm not sure if this is the correct cathegory to place this question in, but there wasn't any that fitted better...
So I have to prove that (7n)! / (7^(n-1) * n! ), for somme integer n, always is equal modulo 7 no matter the value of n...
I've worked out that (7n)! is divible by 7, that 7^(n-1) is as well and that n! would be if n is greater than 7...
But the rest after the division by 7 is not 0, but 6...
Could someone help me please?

 

[stapel]

I have been trying to solve this problem about modular arithmetic now for a long time... I'm not sure if this is the correct cathegory to place this question in, but there wasn't any that fitted better...

I have to prove that (7n)! / (7^(n-1) * n! ), for some integer n, always is equal modulo 7 no matter the value of n.

You have to prove that this expression is equal, mod 7, to what?

I've worked out that (7n)! is divible by 7, that 7^(n-1) is as well and that n! would be if n is greater than 7...
But the rest after the division by 7 is not 0, but 6...

I'm sorry, but I don't understand what you're trying to say here...?

When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!