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GRE 11- How many different ways can 3 cubes be painted if each cube is painted...

By spartan
How many different ways can 3 cubes be painted if each cube is painted one color and only the 3
colors red, blue, and green are available? (Order is not considered, for example, green, green, blue is
considered the same as green, blue, green.)
(A) 2
(B) 3
(C) 9
(D) 10
(E) 27

Clearly, there are more than 3 color combinations possible. This eliminates (A) and (B). We can also
eliminate (C) and (E) because they are both multiples of 3, and that would be too ordinary, too easy, to be
the answer. Hence, by process of elimination, the answer is (D).
Let’s also solve this problem directly. The following list displays all 27 (= 3⋅ 3⋅ 3) color combinations
possible (without restriction):
RRR BBB GGG
RRB BBR GGR
RRG BBG GGB
RBR BRB GRG
RBB BRR GRR
RBG BRG GRB
RGR BGB GBG
RGB BGR GBR
RGG BGG GBB
If order is not considered, then there are 10 distinct color
combinations in this list. You should count them

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