From the wikipedia article on the Republic of Venice.
By 1410, Venice had a navy of 3,300 ships (manned by 36,000 men)
Those numbers don't seem to make sense to me. Surely even a merchant vessel would have more than a dozen crew and it was my understanding that Venetian galleys had at least 70 men including all the rowers and sometimes several hundred crew for the big ones. Were a lot of them very small ships (and if so, what kind of ships were they), were some ships not crewed (why build more ships than you have men to crew) or are those figures simply wrong?
to /u/LooksatAnimals and i'll also tag /u/AlviseFalier
I have once tried to track down this number, and found the best short discussion of it's origin and veracity in Frederic Lane (he is authority for Venetian ships and shipbuilding) and appendix II of his book Venetian Ships and Shipbuilders of the Renaissance (link to Google Book fragment)
Basically, the number of 3,300 is taken from writing of Doge Mocenigo who gives the number of 3,300 (or 3,345 actually) as a rough count of all ships, small and big, owned by Venetians, not specifically state owned "navy". Think of it more as a total count of all ships rather then purely military vessels.
Mocenigo divides the ships in three categories:
Lane tries to verify such numbers and finds them plausible (if maybe slightly large) For example, crew count for galleys is given by Mocenigo is 244 per galley, while Venetian senate orders state they should have 212 men per galley. The small discrepancy shouldn't bother us. Lane also counts that every year Venice sent out at least 16 galleys on commercial voyages ("Romania and Tana -3 , Alexandria -3, Beirut - 4, Flanders and England - 4, Aigues Mortes - 2") and also had at least 10 war galleys each year on patrol duties, so total of 26 per year minimum. Add a few private galleys and the fact that Venice had extra galleys for time of war and the number of 45 isn't out of the ballpark.
For the "navi" ships Lane concludes those are all ships above 100 tons (400 Venetian botte), and them being crewed by 20-30 men is very ordinary. Their number of 300 is really hard to verify though, but given that 100 ton size isn't that large, and those ships were mostly utilized in trade in Adriatic and between closer Venetian possessions, it is a possiblity.
In the end, smallest ships of under 100 tons and crewed by 5-6 men is entirely possible. Those were the numerous small fishing vessels, and small ships utilized by local populations to move around and do various everyday stuff, so it shouldn't really be strange. I think nobody really ever counted them, but putting them in the thousands wouldn't be strange. However those ships would never be a part of a war fleet as such (except as auxiliary vessels)
Although it's actually possible to man a good-sized ship with a surprisingly small crew, I don't have my copy of John Julius Norwich's *History of Venice* (Wikipedia's source for the assertion) with me to evaluate the claim. I did write this older answer on the Venetian Navy some time back which might interest you. In any case, given the ad-hoc nature of rounding up men and material for warfare, especially naval warfare, the claim could either refer to the total number of mobilized ships in a specific instance, or the total number of ships available for mobilization to which specially constructed war-galleys would be added (I might lean towards the former). In any case, it seems the number would exclude mobilized manpower not specifically manning the ships, that is to say soldiery both for defense on-board and transport.