In the study, we aim to investigate the electronic and optical properties of single excitons, biexcions and triexcitons in a CdSe/ZnS core/shell quantum dot nanocrystal. The electronic structure has been determined by solving of the Poisson-Schrodinger equations self-consistently. In calculations, the exchange-correlation effects between identical particles have been taken into account in the frame of the local density approximation. We have demonstrated that the optical properties of triexciton systems are remarkably different from the single and biexciton systems. Absorption peaks or transition energies of the triexciton system are well separated from those of single- and bi-exciton systems. We have observed that the core-radius dependent transition energy variations of triexcitons are higher when compared with single- and bi-excitonic systems. The transition energy shifts of double and triple excitons with respect to the single exciton have been calculated as a function of the core radius and we have shown that the energy shifts are inversely proportional with the radius. We have also investigated the radius-dependent changes in binding energies and lifetimes of the structures and the comparative results have been discussed in a detail manner.