In data center networks, the reliability of Service Function Chain (SFC)—an end-to-end service presented by a chain of virtual network functions (VNFs)—is a complex and specific function of placement, configuration, and application requirements, both in hardware and software. Existing approaches to reliability analysis do not jointly consider multiple features of system components, including, (i) heterogeneity, (ii) disjointness, (iii) sharing, (iv) redundancy, and (v) failure interdependency. To this end, we develop a novel analysis of service reliability of the so-called generic SFC, consisting of n = k + r sub-SFCs, whereby k≥ 1 and r≥ 0 are the numbers of arbitrary placed primary and backup (redundant) sub-SFCs, respectively. Our analysis is based on combinatorics and a reduced binomial theorem—resulting in a simple approach, which, however, can be utilized to analyze rather complex SFC configurations. The analysis is practically applicable to various VNF placement strategies in arbitrary data center configurations, and topologies and can be effectively used for evaluation and optimization of reliable SFC placements.