Ensembles are constructed in the ground-state non-interacting density functional theory. The ensemble Euler equation is formulated as a one-particle Schrödinger-like equation for the square root of the ensemble density. The potential in this equation is the sum of the original Kohn-Sham potential plus the ensemble Pauli potential. The latter satisfies a first-order differential equation. The true electron density can be easily obtained from the ensemble electron density. The ensemble density or the ensemble non-interacting energy density or the ensemble angular momentum density provide a full description of a Coulomb system.