# Math Help - Simplify factorial containing only variables : possible ?

1. ## Simplify factorial containing only variables : possible ?

Hi,

I'm writing here tonight to ask you if it's possible to simplify this :

$\frac{z!}{(z-e)!}$

My colleague and I are intrigued in a homework about how someone got to a very different solution that does also work... we're trying to see if we can simplify some stuff.

If you dare try to simplify out stuff... here it is :

$\frac{n!}{(n-k)!k!} \sum\limits_{e=0}^{\frac{k(k-1)}{2}} \frac{\frac{k(k-1)}{2}!}{(\frac{k(k-1)}{2}-e)!e!}$

You probably understood that $z=\frac{k(k-1)}{2}$

2. ## Re: Simplify factorial containing only variables : possible ?

Is e a variable or Euler's number?

3. ## Re: Simplify factorial containing only variables : possible ?

Hi,

It's a variable, it stands for "edge" are this formula calculates the number of subgraphs of k vertex in a complete graph Kn.