Use of Genitive

[Carvalho]

For example in this sentence:
We all met at the house of Olivia to plan a campaign against factory arms.
Can we say:
We all met at Olivia's to plan a campaign against factory arms.
Is it a rule to omit House or can we say:
We all met at Olivia's house to plan a campaign against factory arms.

Thanks for your help! :?

[Mister Micawber]

The first one ('house of Olivia') in not used. The other two are fine.
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Native English teacher at Mister Micawber's