Which of the following is an example of probable cause that would allow police to enter a private home without a warrant?

One example would be exigent circumstances, such as:

An officer is dispatched to a report of a loud argument at a certain house. He arrives and hears screams coming from inside the house. He looks through the window and sees one person assaulting another. The police officer now has probable cause to believe that immediate entry into the house is necessary because someone inside the house is being hurt.

There are many other examples, but the all boil down to one of the following:

1. Consent

2. Exigent circumstances

3. Plain view

4. Incident to arrest

5. When in "hot pursuit" of a fleeing criminal.