WMC 2018 Senior Problem 39

Level 2

Miquel has 5 5 colors of paint and wants to paint the 4 4 walls of his bedroom. He randomly picks the colors but insists that no 2 2 adjacent walls are the same color. What is the probability that exactly 2 2 of the walls will be painted the same color?

1 2 \frac{1}{2} 6 13 \frac{6}{13} 3 5 \frac{3}{5} 5 12 \frac{5}{12} 7 13 \frac{7}{13}

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