It seems that if A, B and C are the only possibilities for column C and you want to count all 3 possibilities then you are merely counting how many cells are occupied so you can simply use:
=COUNTIFS($B$3:$B$20,"Full",$C$3:$C$20,"*")
and
=COUNTIFS($B$3:$B$20,"Part",$C$3:$C$20,"*")