In this paper, we examine and extend the Finite Selection Model (FSM) of Morris (1979) for randomly allocating units to multiple treatment groups in experiments. The FSM lets each treatment group take turns in a fair and random order to select units from a sample such that, each treatment optimizes for its own group without hurting the other treatment groups. In this paper, we formalize the FSM under the potential outcomes framework. We use an algorithm named SCoMaRS to determine the selection order of treatments and show that SCoMaRS is the unique sequentially controlled Markovian algorithm for generating a selection order. We discuss its extensions to multi-treatment and stratified settings. We propose a selection criterion based on the idea of D-optimality and discuss its theoretical implications. We illustrate FSM's performance using simulation studies and actual randomized experiments. The FSM systematically provides adequate covariate balance under the correct specification of the outcome model and robustness under model misspecification. Moreover, we show that with certain choices of the selection order and selection criteria, the FSM retrieves several classic designs.