Product families help companies reach customers in several different markets, lessen the time needed to develop new products, and reduce costs by sharing common components among many products. The product platform can be considered as a set of technologies, components, or functions, and their arrangements, that are utilized for more than one product. Configuration design focuses on the components in a product and their connections and relationships. Discrete, combinatorial design spaces are used to model design requirements regarding physical connections, module partitions, and assembly sequences for the product family. To ensure that products satisfy all design requirements, it is necessary to combine these design spaces into a common configuration space into which all requirements can be mapped. This paper presents computational methods for modeling and combining design spaces so those configurations can be identified that satisfy all constraints. A new representation of assembly sequences facilitates the development of an assembly design space, elements of which can be enumerated readily. Because the size of the combinatorial design spaces can become quite large, computational efficiency is an important consideration. A new designer guided method, called the partitioning method, is presented for decomposing configuration design problems in a hierarchical manner that enables significant reductions in design space sizes. An example of a family of automotive underbodies illustrates the application of the discrete design space approach to develop a common platform.