The electronic structure of the CuO{sub 2} planes and CuO{sub 3} chains in single-domain crystals of YBa{sub 2}Cu{sub 3}O{sub {ital x}} has been investigated as a function of oxygen concentration (6{le}{ital x}{le}7) using polarization-dependent x-ray-absorption spectroscopy of the O 1{ital s} and Cu 2{ital p} core levels. The polarization-dependent observation of unoccupied states with O and with Cu orbital character parallel to the {ital a}, {ital b}, and {ital c} axes of the crystals allows the determination of the number of hole states in Cu 3{ital d}{sub {ital x}}{sup 2}{minus}{ital y}{sup 2} and O 2{ital p}{sub {ital x},}{ital y} orbitals in the CuO{sub 2} planes as well as in Cu 3{ital d}{sub {ital y}}{sup 2}{minus}{ital z}{sup 2} and O 2{ital p}{sub {ital y},}{ital z} orbitals in the CuO{sub 3} chains. States with Cu 3{ital d}{sub 3{ital z}}{sup 2}{minus}{ital r}{sup 2} orbital character contribute less than 10% to the total number of states near the Fermi level. The number of holes in the planes and in the chains is found to be correlated with the superconducting transition temperature.