This question already has an answer here:
Other questions have looked into founding successful colonies, meaning healthy populations that thrive indefinitely. However, many stories concern a colony that is discovered some specific (and historically short) time after it is started.
In Star Trek: The Next Generation and Fallout 3 both featured a group of shut ins where in the former (Season 5 episode 13 The Masterpiece Society) was planned from the start and the latter (Vault 101) was an emergency measure to a nuclear holocaust. Both lasted for about 200 years and both were noted to still have a diverse enough gene pool with plans for selective breeding (it being brought up by the Vault 101 Overseer when you have a high enough intelligence skill).
Now assuming that a Vault or Colony had the right equipment/policies to avoid a skills shortage and there were no accidental deaths, how many people minimum (how many males/females, how many would need to be adults/children at the beginning) would be needed to have a diverse enough gene pool to last about 2 centuries?
That is, when visitors arrived 200 years later, they found living descendants of the original small population.