They forgot about Cryopreservation as an option.
They could take even LESS human bodies (and thus a much smaller ship) by doing that way. You could have about only 5,000 people (mostly women) in states of suspended animation, and take BILLIONS of sperm and egg in suspended animation as well. Once landed on a habitable planet it will be the job of the awoken birthers to have a few humans. And by using donor egg and sperm, you can create a whole society of non-siblings that can then breed with one another. The ship can be kept going mostly by computers with generations of crew members to assist. Other than that, NO ONE gets to go. Not very pretty... but survival rarely is.
http://en.wikipedia.org/wiki/Suspended_animation
Listen!.... You smell something?