A bag contains some marbles, each of which is one of four colors (red, white, blue, and green). There is at least one of each color. The composition of the bag is such that if we take four marbles out at random (without replacement), each of the following is equally likely:
(1) one marble of each color is chosen,
(2) one white, one blue, and two reds are chosen,
(3) one blue and three reds are chosen,
(4) four reds are chosen.
What is the smallest possible number of marbles in the bag?
