Twenty swimmers are competing in the Olympics. Of the swimmers, 6 are from the United States, 4 are from Canada, 3 are from China, 4 are from Japan and 3 are from Russia. Suppose the scoring takes account of the countries that the swimmers represent, but not their individual identities. What is the probability that the United States has 3 competitors in the top ten and 3 competitors in the bottom ten? (You may assume that each swimmer is equally likely to do as well as any other swimmer. You may also assume there are no ties).