Combinatorial networks are widely applied in many practical scenarios. In this paper, we compute the closed-form probability expressions of successful decoding at a sink and at all sinks in the multicast scenario, in which one source sends messages to k destinations through m relays using random linear network coding over a Galois field. The formulation at a(all) sink(s) represents the impact of major parameters, i.e., the size of field, the number of relays(and sinks) and provides theoretical groundings to numerical results in the literature. Such condition maps to the receivers’ capability to decode the original information and its mathematical characterization is helpful to design the coding. In addition, numerical results show that, under a fixed exact decoding probability, the required field size can be minimized. Combinatorial networks are widely applied in many practical scenarios. In this paper, we compute the closed-form probability expressions of successful decoding at a sink and at all sinks in the multicast scenario, in which one source sends messages to k destinations through m relays using random linear network coding over a Galois field. The formulation at a (all) sink (s) represents the impact of major parameters, ie, the size of field, the number of relays (and sinks) and provides theoretical groundings to numerical results in the literature. Such condition maps to the receivers’ capability to decode the original information and its mathematical characterization is helpful to design the coding.