The correct answer is 'Community cloud', as this model provides a cloud computing environment where the infrastructure and services are shared among several organizations from a specific group with common computing concerns, such as security, compliance, jurisdiction, etc., which fits the needs of a consortium of educational institutes. A 'Public cloud' would not offer the exclusive shared environment tailored to their common needs. Though a 'Private cloud' would provide the security and compliance they require, it wouldn't be shared among the institutions. 'Hybrid cloud' is incorrect because it refers to a combination of private and public clouds, designed to facilitate a flexible, optimized environment, which may be more complex than needed for their purpose.