Meaning of \({ _{ n }{ P }_{ r } }\)

What positive integers \(m\) and \(n\) satisfy the following two equations: \[ m\cdot { P }_{ 5 }^{ n }=72 \cdot { P }_{ 3 }^{ n }, \quad { P }_{ 6 }^{ n }=m \cdot { P }_{ 4 }^{ n }? \]

Details and assumptions

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