Question

How many electrons are allowed to share the same quantum state according to the Pauli Exclusion Principle?

Answer 1

Two.

Explanation:

One can have "spin up" with the spin quantum number `m_s=+1/2`, the other would then have "spin down" with `m_s=-1/2`. The Pauli Exclusion Principle allows that but no more.

Answer 2

2 electrons

Explanation:

Only 2 electrons, both belong to 3px orbital.
Both the electrons have all the three quantum numbers same, i.e they belong to same shell, same sub shell and same orbital but differ in their spins i,e the spins are opposite or spin quantum number is different as per EXCLUSION PRINCIPLE of PAULI.