AHSME 1996 Problem 26

An urn contains marbles of four colors: red, white, blue, and green. When four marbles are drawn without replacement, the following events are equally likely: (a) the selection of four red marbles; (b) the selection of one white and three red marbles; (c) the selection of one white, one blue, and two red marbles; and (d) the selection of one marble of each color. What is the smallest number of marbles satisfying the given condition? $\text{(A)}\ 19 \text{(B)}\ 21 \text{(C)}\ 46 \text{(D)}\ 69 \text{(E)}\ \text{more than 69}$