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

The given expression is \( \frac{N!}{(N-x)!} \). To simplify this expression, we can use the property of factorials that \( N! = N \times (N-1) \times (N-2) \times \ldots \times 2 \times 1 \). Therefore, \( \frac{N!}{(N-x)!} = \frac{N \times (N-1) \times (N-2) \times \ldots \times (N-x+1)}{(N-x) \times (N-x-1) \times \ldots \times 2 \times 1} \). This simplifies to \( \frac{N \times (N-1) \times (N-2) \times \ldots \times (N-x+1)}{(N-x) \times (N-x-1) \times \ldots \times 2 \times 1} \). 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: \(\frac{N!}{\left(N-x\right)!}\) The simplified expression is \( \frac{N!}{(N-x)!} \).