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Prove by permutations or otherwise $\displaystyle \frac{\left(n!\right)!}{\left(n!\right)^{(n-1)!}}$, where $n\in \mathbb{N}$
The discussion centers on the mathematical expression $\displaystyle \frac{\left(n!\right)!}{\left(n!\right)^{(n-1)!}}$ and its evaluation as an integer for natural numbers $n$. Participants clarify that the question lacks specificity regarding the proof required. It is established that this inquiry is not novel, as it mirrors previous discussions on similar factorial expressions.
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