Peter purchased a pentagonal pen for his puppy Piper. Now Peter wants to decorate the new pen for Piper, and he would like to paint each side of the pen either red, green, or blue so that each wall is a solid color.
(Pentagon here with top vertex is A and B is to the left and so on)
Peter can only paint at night when Piper is sleeping, and unfortunately it is too dark for him to determine which color he is painting. So for each wall, Peter randomly chooses a can of paint and paints the wall in that color. In the morning, Peter observes the resulting color scheme. The vertices of the pentagon are labeled with the letters A, B, C, D, and E, and these labels are clearly visible during the daytime. What is the probability that no two adjacent walls of the pen have the same color?
Please explain your answer a little bit at least it would help very much! Please responnd quick also :)