Elementary particles such as Quarks obey Pauli's exclusion principle since they exist in three colors (RBG). Where as electrons which is also elementary that does not have any color quantum numbers obey Pauli's exclusion principle. Any one please explain why.
Pauli's exclusion principle applies to any particle which has a half integer spin.
Pauli first proposed his principle to explain the behaviour of electrons in atoms, and it was later found to apply to other spin 1/2 particles.
Spin 1/2 particles form a category called 'Fermions' (named after Enrico Fermi). Particles with integer spin are called 'Bosons' (named after Satyendra Bose).
Fermions can behave like Bosons in certain combinations. For example, a 'Cooper pair' of electrons.
No two electrons in an atom can have identical quantum numbers. This is an example of a general principle which applies not only to electrons but also to other particles of half-integer spin (fermions). It does not apply to particles of integer spin (bosons).
Elementary particles such as Quarks obey Pauli's exclusion principle since
they are fermions. That is the correct continuation of the sentence.
they exist in three colors (RBG).
That is correct, the colors are three quantum numbers that can distinguish quarks ( which are fermions) between them, so if they have a different color they are allowed to be in the same quantum state because the color quantum number makes them non identical.
Whereas electrons which is also elementary that does not have any color quantum numbers obey Pauli's exclusion principle. Any one please explain why.
Pauli's exclusion principle for electrons as applied to atomic physics is one of the cases of the exclusion principle in quantum mechanics, two fermions of exactly the same quantum numbers cannot occupy the same energy level, in a quantum mechanical system. A red quark is as different from a blue quark as an electron from a muon .