Explanation
According to "The NIST Definition of Cloud Computing," in PaaS, "the capability provided to the consumer is to deploy onto the cloud infrastructure consumer-created or acquired applications created using programming languages, libraries, services, and tools supported by the provider. The consumer does not manage or control the underlying cloud infrastructure including network, servers, operating systems, or storage, but has control over the deployed applications and possibly configuration settings for the application-hosting environment.

Public clouds offer services to anyone, regardless of affiliation, and are the most likely to offer free services to users. Examples of public clouds with free services include iCloud, Dropbox, and OneDrive.
Private cloud models are designed for specific customers and for their needs, and would not offer services to the public at large, for free or otherwise. A community cloud is specific to a group of similar organizations and would not offer free or widely available public services. A hybrid cloud model would not fit the specifics of the question.