SOLUTION: 7 fence boards are being painted from both sides and each side of an individual board gets its color picked randomly. What is the probability of exactly 3 fence boards being colour

Although it is not pronounced in the problem, I will assume that in this problem there are 7 base colors.


Then this experiment is the binomial distribution with the probability 1/7 for each fence board 
to be painted the same color from both sides, and with the probability 6/7 for each fence board
to be painted in different colors.


So the number of trials is 7; the probability of a success trial is 1/7 and the probability of 
unsuccess trial of 6/7. They ask about the probability to have 3 success trials.


    P =  =  = 0.055079  (rounded).   ANSWER