Final answer:
The primary purpose of forming alliances between countries is mutual support against a common threat, often with shared military or economic aims to increase security and prosperity among member states.
Step-by-step explanation:
The primary purpose of forming alliances between countries is c) Mutual support against a common threat. Alliances serve to unite nations in both military and economic efforts to confront shared challenges or adversaries. Whether these challenges are military threats from other nations or terrorist groups, or economic threats such as boycotts and high tariffs, alliances typically aim to provide a collective response to secure the safety and prosperity of their member states. This rationale was evident during World War II, when alliances were formed to fight against common enemies, and it continues to be a driving force behind contemporary partnerships formed to counter terrorist threats or promote trade.