You can read the story of Noah(AS) in these six chapters of Qur'an:
- Al-'A`raf(7)
- Hud(11)
- Al-Mu'minun(23)
- Ash-Shu`ara'(26)
- Al-Qamar(54)
- Nuh(71)
and the most detailed one is the Hud chapter in which you can read about Noah(AS) in 25 verses( verse 25 to 49).
in verse 11:40, Quran states:
حَتَّىٰ إِذَا جَاءَ أَمْرُنَا وَفَارَ التَّنُّورُ قُلْنَا احْمِلْ فِيهَا مِن كُلٍّ زَوْجَيْنِ اثْنَيْنِ وَأَهْلَكَ إِلَّا مَن سَبَقَ عَلَيْهِ الْقَوْلُ وَمَنْ آمَنَ ۚ وَمَا آمَنَ مَعَهُ إِلَّا قَلِيلٌ
[So it was], until when Our command came and the oven overflowed, We said, "Load upon the ship of each [creature] two mates and your family, except those about whom the word has preceded, and [include] whoever has believed." But none had believed with him, except a few.
so from the part "whoever has believed" we can understand that some other people were also in Noah's(AS) ship and they did survived, so even if there were no people living in other parts of the world(I can't remember any verse proving these ones), we may be descendents of those other believers.