The edges of a regular pentagon are colored red, blue, or green at random, so that each edge has an equally likely chance of being painted with any given color. What is the probability that in the resulting coloring, no two adjacent edges have the same color?
You can't have 0 reds.
You can have 1 red, and there are 2 scenarios for that.
You can have 2 reds, and there are 8 scenarios for that.
You can't have 3+ reds.
In total, there are 10 scenarios that work. There are 3^5 - 3 total cases, so the probability is 10 / 240 = 1/24