Add this all up and you get 21,500 different species. Of course, there were two of each, or 43,000 individuals on the boat. That sounds like ample space. A bit cramped, but a possibility. This would take up quite a bit of space, as they were supposedly on the ark for at least 275 days.
Water storage is a big problem.
After all, you can't drink the salty seawater. If we figure an average of 1 quart per day for each animal, Noah would have to store away 1,263,125 gallons of the liquid. Of course, it was raining quite heavily, so the supply could have been considerably less. Let's not forget the space needed for cages, partitions, and passageways. We need even more space for any offspring produced along the way.