Use "vain hope" in a sentence

1. I knocked loudly in the vain hope that someone might answer.

2. The doctors gave him more powerful drugs in the vain hope that he might recover.

3. Guided by a mournful bleating, he came across several groups of sheep, huddled together in the vain hope of safety.

4. Better than enduring his fumbling during the night in the vain hope of satisfaction when the need was strong in her.

5. And plans are afoot to turn the bureau into an independent agency, in the probably vain hope that this would free it from politics.