How many starships does Starfleet have?

[AKAArzosah]

[color=#000000ost_uid0]There is a difference between 'Federation' Ships and 'Star Fleet' Ships. If you count all the ships in the Federation, there has to be at least a couple thousand ships, but not many of them would be controlled by Star Fleet.
Many cargo ships would be privately owned, or owned by a company, and some of the Federation's science and exploratory vessels would just be scientists, not military.
Think of the resources needed to build all those ships. They may not technically cost anything, but you need to have something to make them out of. Can they replicate everything? I doubt it.

Also, hadn't the Federation been building more ships for years during the Dominion War, building up strength for the final attack? First Contact was before that, too.[/colorost_uid0]