(1) Suppose there are n judges scoring, remove the highest score and the lowest score, then add up the scores of the remaining (n-2) judges and divide them by (n-2), and then compare the sizes. The highest score is the champion, the second highest is the runner-up and the third highest is the runner-up.

(2) First of all, the champion and runner-up are two special elements. At this time, there are three situations. First, if there is a champion, just choose one of the remaining four players; Second: including the runner-up, as above, also choose one from the remaining four players; Third: the two people selected are the champions and runners-up, and there is only one way to choose. These are three ways to do it, using addition, and then this question doesn't involve order, just combination. So the answer is (c 41+c 41+1)/C62 = 9/15 (I hope you can understand the combination number).