An analytical solution is successfully derived for a simplified model of the solute redistribution without back diffusion during dendritic solidification of a binary alloy in which the dendrite arm coarsening is incorporated. The solution essentially includes the Scheil equation as a subset. Calculated results for typical cases reveal that the dendrite arm coarsening affects the microsegregation significantly in that the eutectic fraction predicted for an expanding domain is considerably smaller than that for a fixed arm spacing. The most important feature of the results reported in comparison to the Scheil equation lies in the fact that there exists a lower limit of the initial concentration below which the eutectic is not formed. Based on the present results, a new regime map for the eutectic formation state on the initial concentration-equilibrium partition coefficient plane is proposed. The map, which is bounded by the solubility limit and diffusion controlled limit curves, consists of three regions : the eutectic not formed, conditionally formed and unconditionally formed.