$$ \frac { N ! } { ( N - x ) ! } = $$

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The given expression is $$ \frac{N!}{(N-x)!} $$.

To simplify this expression, we can use the property of factorials that $$ N! = N 	imes (N-1) 	imes (N-2) 	imes \ldots 	imes 2 	imes 1 $$.

Therefore, $$ \frac{N!}{(N-x)!} = \frac{N 	imes (N-1) 	imes (N-2) 	imes \ldots 	imes (N-x+1)}{(N-x) 	imes (N-x-1) 	imes \ldots 	imes 2 	imes 1} $$.

This simplifies to $$ \frac{N 	imes (N-1) 	imes (N-2) 	imes \ldots 	imes (N-x+1)}{(N-x) 	imes (N-x-1) 	imes \ldots 	imes 2 	imes 1} $$.

We can further simplify this expression by canceling out the common terms in the numerator and denominator.

Let's calculate the simplified expression.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{N!}{\left(N-xight)!}$$
The simplified expression is $$ \frac{N!}{(N-x)!} $$.
The simplified expression is $$ \frac{N!}{(N-x)!} $$.

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