Exclusion Principle: Do Similar Sub-Atomic Particles Follow?

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Does the exclusion principle hold true only for similar sub-atomic particles?
 
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It holds only for identical fermions.
 
Alright. But then how is that proton stars are formed due to the exclusion principle repulsion between protons and neutrons and simple dwarf stars are formed due to the exclusion principle repulsion between electrons? Why these reservations? Or do special conditions prevail?
 
This means that a star with mass above the Chandreshekhar limit may either collapse into a black hole or a neutron star, depending upon the amount of pressure.
 
I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...

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