We study the quantum plasmonic features of gold and silver nanoparticles using TD-DFT+TB, a new density functional theory approach to the calculation of excited states, which combines a full DFT ground state with tight-binding approximations in the linear response calculation. In this framework, the optical properties of closed-shell Ag, Au and bimetallic Ag-Au nanoparticles with tetrahedral symmetry (with 20, 56, 120, and 165 atoms) and icosahedral structure (with 13, 55, and 147 atoms) were obtained and compared to full linear response time-dependent density functional theory (TD-DFT) as a reference and also to time-dependent density functional based tight binding (TD-DFTB) as a low-cost alternative approach. We find an excellent agreement of TD-DFT+TB calculated absorption spectra with the TD-DFT reference with errors less than 0.15 eV in peak positions, while TD-DFTB shows larger errors of about 1 eV. The computational cost for the ground state calculation is identical for TD-DFT and TD-DFT+TB, but the excited state calculation becomes about a hundred times faster when applying the TB approximation and is then almost negligible for the overall timing of the calculation. In contrast to TD-DFTB, which can only be applied to element combinations for which a suitable DFTB parametrization is available, TD-DFT+TB can be applied to any combination of elements. To assess the accuracy of TD-DFT+TB for different combinations of atoms, the plasmonic properties of bimetallic clusters with different ratios of Ag and Au atoms were obtained and the trend of energy and intensity reproduced in good agreement with TD-DFT, which is not possible using TD-DFTB with standard parameter sets.