167.Red, Green, Blue at a Corner
★★★classical probabilityCh. 1 — Classical Probability and Combinatorics444+ Problems in Probability
The 6 faces of a cube are each painted a distinct color among red, blue, green, yellow, purple, and pink. Find the probability that the faces colored red, green, and blue all share a common vertex of the cube.
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Three faces share a vertex exactly when no two of them are opposite faces. Count the face-triples at the cube's 8 corners.
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