To pick 4 balls without replacement, and with at least one of each color, there are 3 cases: (1) 2 red, 1 green, and 1 yellow; (2) 1 red, 2 green, and 1 yellow; (3) 1 red, 1 green, and 2 yellow.  These 3 cases do not overlap, so you can count them separately, and add them up.