Noah and his household would be saved because:
for you alone I have seen to be righteous before Me in this time. (Genesis 7:1)Noah and his household would be saved because Noah found favor in the eyes of the Lord (Genesis 6:8). Noah was a righteous man, blameless in his time; Noah walked with God. (Genesis 6:9) Noah was seen to be righteous. And why was Noah seen to be righteous? Was it because he was perfect? Was it because he was without sin? No!
Noah was seen to be righteous because of Christ. Noah, as is stated in Hebrews 11, gained God’s approval by faith (Hebrews 11:7). Noah walked by faith:
Now faith is the assurance of things hoped for, the conviction of things not seen. For by it the men of old gained approval. By faith we understand that the worlds were prepared by the word of God, so that what is seen was not made out of things which are visible. (Hebrews 11:1-3)Noah did not love the world nor the things in the world. (1 John 2:15) Noah did not spend his life in pursuit of the lust of the flesh and the lust of the eyes and the boastful pride of life— for all of those things are from the world! The rest of the pre-flood world pursued those things! The rest of the pre-flood world pursued after that which would pass away, but Noah strived to do the will of his Creator. Noah walked with God— he trusted in God, and his faith was credited to him as righteousness.
After 120 years, the ark was ready. Noah and his household would be saved, but the rest of mankind would plunge into destruction. The rest of the pre-flood world would not enter the ark. The rest of the world did not walk by faith. Justice was about to be poured out upon man, and only because of Christ did humanity persevere.
Summary of Genesis 6
Noah's Obedience - Genesis 6:22
State Of The World (2469 BC): 120 Years Before The Flood - Genesis 6:3
God's Covenant With Noah: Promised - Genesis 6:18