I need your help to resolve a grammar related problem that I often encounter: I become confused about the use of singular and plural in course of writing a sentence.
Examples:
Millions of people are searching for a house for their families in Delhi.
or
Millions of people are searching for houses for their families in Delhi.Many people were trying to get a cup of coffee for themselves, but as cups were less in numbers than the people, so many of them could not get one for them.
or
Many people were trying to get cups of coffee for themselves, but as cups were less in number, so many of them could not get one for them.They all were doing their best to get promotions, but only Jack succeeded to get one for himself.
or
They all were doing very hard to get a promotion, but only Jack succeeded to get one for himself.
Could you please inform which sentences are the right ones and why? And what should I do when I have to write such a sentence.