In this paper we propose an effective method for solving the optimization problem of the redundant allocation and unit selection in system reliability with several failure-modes by using the implicit enumeration algorithm. The quantitative evaluation for the proposed method is indicated clearly. This shows that the number of constraints and variables in the proposed one are few than those of the integer programming method, respectively. Recently, McLeavey points out an example in which an algorithm reported by Ghare and Taylor for determining optimum redundancy in a series system dose not produce an optimal solution. We also report a new optimal solution of the numerical example in which the objective function to be minimized is smaller than and the system reliability is higher than that of the integer programming method, respectively. Consequently, the computer CPU time is shorter than that of the integer programming method with the same computer and implicit enumeration as a solution algorithm.