Why when all are separated by mans sin was Noah chosen? Why, if all are separated from God because of Adam's sin, did God choose Noah?  Why be merciful to Noah's descendants if all are separated by sin?
Genesis 6:5-6 describes God’s view of the people who lived prior to the flood: 


  “The LORD saw how great the wickedness of the human race had become on
  the earth, and that every inclination of the thoughts of the human
  heart was only evil all the time. The LORD regretted that he had made
  human beings on the earth, and his heart was deeply troubled.”  


God determined to wipe out the evil deeds of men and put an end to their wickedness.  


  “But Noah found favor in the eyes of the LORD” (Genesis 6:7, 8).


All the people on earth died except Noah and his family who were found righteous in the eyes of God. The people who perished in the flood died because they refused to acknowledge God or seek His forgiveness. Noah, on the other hand, is described as righteous, blameless, and obedient in that he 


  “walked with God” (Genesis 6:9).  


Noah and his family were not spared because they were without sin, but because Noah was obedient and without blame.  God had a plan and that plan involved Noah and his family. The polluted, unrighteous population of the world of Noah disappeared from the earth. Mankind was salvaged, and from the line of righteous Noah came the Son of Man, Jesus Christ, who died to atone for the sins of the world. [1]

Hebrews chapter 11 gives examples of other imperfect people who were used by God in the outworking of his divine purpose.  They were all sinners, but God enabled them to overcome and to do incredible things to his glory.  

God, in his sovereignty, has the undisputed right to bless and to give, to show mercy and dispense his grace on those whom he favors.  God blessed Abraham (Genesis 12:3) because Abraham believed God, and his faith was credited to him as righteousness (Genesis 15:6).  Noah was righteous and blameless “and he walked with God” (Genesis 6:9). God showed mercy to Noah because he was obedient and his faith in God never wavered.  

[1]Source: The Genesis Flood: The Biblical Record and Its Scientific Implications, 50th Anniversary Edition.  (Dr. John C. Whitcomb, Dr. Henry M. Morris