Romans 5:15 tells us, “But the free gift is not like the transgression. For if by the transgression of the one the many died, much more did the grace of God and the gift by the grace of the one Man, Jesus Christ, abound to the many.” [NASB]
The idea of a federal head is that one person represents many. A president represents an entire nation in one person – even if the people don’t like it. Adam – and then Noah – represented the entirety of mankind’s genetic lineage. They were bound to sin and they could not revert to a federal headship that included righteousness.
That’s why we needed Jesus to come as fully God and fully man. He broke from Adam’s federal headship and created a new, perfect headship in His resurrection
Ephesians 2:6 tells us that when we believe in Jesus Christ as our savior we are born again a new creation in Christ. His grace truly does abound to the many – to all who believe.