The chord progression for the piano part is an F major chord, followed by an A minor chord (changing only one note of the 3 from the F major chord), and then a C major chord (changing only one note from the A minor chord).

So in total of all the 3 chords in the song there are only 5 total notes used, kind of interesting huh?

It seems like chord progressions that share overlapping notes sound better to the human ear for some reason. 3 chords represented in only 5 notes is pretty compact. And the more I look in to it, almost every popular song does the exact same thing. You will almost never see a song that has 3 chords with 9 unique notes, for example.