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Chemical reaction dynamics are studied to monitor and understand the concerted motion of several atoms while they rearrange from reactants to products. When the number of atoms involved increases, the number of pathways, transition states and product channels also increases and rapidly presents a challenge to experiment and theory. Here we disentangle the dynamics of the competition between bimolecular nucleophilic substitution (S(N)2) and base-induced elimination (E2) in the polyatomic reaction F- + CH3CH2Cl. We find quantitative agreement for the energy- and angle-differential reactive scattering cross-sections between ion-imaging experiments and quasi-classical trajectory simulations on a 21-dimensional potential energy hypersurface. The anti-E2 pathway is most important, but the S(N)2 pathway becomes more relevant as the collision energy is increased. In both cases the reaction is dominated by direct dynamics. Our study presents atomic-level dynamics of a major benchmark reaction in physical organic chemistry, thereby pushing the number of atoms for detailed reaction dynamics studies to a size that allows applications in many areas of complex chemical networks and environments.