• C = C(same color) + C(2 colors) + C(3 colors) C(same color)= 3 C(2 colors) = 2R1G + 2R1Y + 2G1R + 2G1Y +2Y1R + 2Y1G =6 choices each of these choices could be ordered with 2 of the same color consecutively at the start, at the end, or one at the start and one at the end. So we actually have 18 possible outcomes when two colors are choosen. The possible outcomes for 3 different colors is the permutation of selecting 3 different marbles: C(3 colors)= 3P3= 6 so there are a total of 30 choices

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