High data acquisition rates and low-noise detection of ultracold neutral atoms present important challenges for the state tomography and interferometric application of entangled quantum states in Bose-Einstein condensates. In this paper, we present a high-flux source of
87Rb Bose-Einstein condensates combined with a number-resolving detection. We create Bose-Einstein condensates of $2\ifmmode\times\else\texttimes\fi{}{10}^{5}$ atoms with no discernible thermal fraction within 3.3 s using a hybrid evaporation approach in a magnetic and optical trap. For the high-fidelity tomography of many-body quantum states in the spin degree of freedom [M. Hetzel, et al., arXiv:2207.01270], it is desirable to select a single mode for a number-resolving detection. We demonstrate the low-noise selection of subsamples of up to 16 atoms and their subsequent detection with a counting noise below 0.2 atoms. The presented techniques offer an exciting path towards the creation and analysis of mesoscopic quantum states with improved fidelities and towards their exploitation for fundamental and metrological applications.