How could 100 different cultures scattered throughout the world have the same story if the only people that survived were from just one of those cultures?
The diaspora during the building of the Tower of Babel occurred after the flood. So, Noah survived the flood, the story was passed to his descendants. Noah's descendants tried to build a tower to reach to Heaven.
God confused their tongues. The people spread out with different languages and started different cultures.....all descending from Noah; all with knowledge of the flood.
Read Genesis 9-11.
The Reader's Digest Version:
Eight people survive the Flood and land on Mt. Ararat. Noah, Mrs. Noah, Noah's 3 sons (Japeth, Shem, Ham), and their 3 wives. They have children, and they spread across the earth.
Over time, the stories they heard from their grandfathers, and great grandfathers get a bit corrupted/twisted along the way. Thus you have the same story, but with slight variations or embellishments.
God kept the original facts by using one family, the Hebrews, to be the keepers of His Oracles (God's Word) until the time of Christ. So, even though the Hebrews and non-Hebrews came from the same family (all from the ark that landed at Mt. Ararat), only the Biblical version was left intact because God protected it -- so mankind would always have a record of His message and love.
Genesis 11:11 And the whole earth was of one language, and of one speech.
2 And it came to pass, as they journeyed from the east, that they found a plain in the land of Shinar; and they dwelt there.
3 And they said one to another, Go to, let us make brick, and burn them thoroughly. And they had brick for stone, and slime had they for morter.
4 And they said, Go to, let us build us a city and a tower, whose top may reach unto heaven; and let us make us a name, lest we be scattered abroad upon the face of the whole earth.
5 And the Lord came down to see the city and the tower, which the children of men builded.
6 And the Lord said, Behold, the people is one, and they have all one language; and this they begin to do: and now nothing will be restrained from them, which they have imagined to do.
7 Go to, let us go down, and there confound their language, that they may not understand one another's speech.
8 So the Lord scattered them abroad from thence upon the face of all the earth: and they left off to build the city.
9 Therefore is the name of it called Babel; because the Lord did there confound the language of all the earth: and from thence did the Lord scatter them abroad upon the face of all the earth.