Meaning of $${ _{ n }{ P }_{ r } }$$

Discrete Mathematics Level 2

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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