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Random Crayons

At a restaurant, two children each receive a packet of four crayons, each a
different color. They combine their crayons (to make four pairs) and line
them up randomly on the table. What is the probability that all pairs of
adjacent crayons are different colors? Repeat for two and three pairs of
crayons.

Source: It just, uh, came to me...

Solution

Mail to Ken