You can go to a great deal of unnecessary work with this problem if you don't notice that the first and second transfer are meaningless except to mix you up.
The problem can be restated like this: Given twenty-four marbles, of which eight are blue, eight red, and eight yellow, how many must you select to be sure of having at least three of each color?
The answer is obviously 8+8+3, or 19. Five marbles were left in Bag 2.