I am trying to solve a probability question.
5 people are competing in a cooking competition and there are 3 raters. Each person will cook 4 dishes and the dishes will be rated from 0 (bad) to 10 (good). I would like to determine the probability that two raters always rate within 5 points of each other for the 4 dishes for the five people.
Please could we not get into the advanced topics such as reliability of the raters and so on. My initial thought was to apply principle of inclusion/exclusion. So first compute the probability for each individual question and then multiple all these probabilities to the the final answer. I thought I did something like this in high school or college, but cannot really comprehend the answer. Can anyone solve this? Some steps of explanation are highly appreciated.