Correct on the first part waaaay wrong on the second.
Actually, you don't even need dinosaurs to far exceed any conceivable ark no matter how you convert it.
Two of every species would have to inlcude EVERY species alive today, as well as every species since the flood that has gone extinct.
EVERY SPECIES
[culled from various websites, using google searches of "insect species", etc]
Insects
There are about 900,000 known insect species, three times as many as all other animal species together, and
thousands of new ones are described each year.
Birds
8000+ species identified and currently living.
Mammals
4629 currently recognized species of mammals.
Marsupials
Depending on the classification system used, scientists have identified between 260 and 280 species of marsupials
Reptiles
8000+ species
Etc.
This is just what is KNOWN.
We have over 1.3M species of what would have to have been carried on a hypothetical ark.
Wikipedia count of species
Let's be generous and say we know about 75% of all those species.
1.3/.75=1.73
Noah's ark carried AT LEAST 1.73 million different species, AND somehow deposited them in biologically similar groupings (notice any marsupials in europe?), with land-locked species distributed over every continent and islands not connected to Eurasia.
Um, right.