In a soccer tournament of 15 teams, the top three teams are awarded gold, silver, and bronze cups, and the last three teams are dropped to a lower league. We regard two outcomes of the tournament as the same if the teams that receive the gold, silver, and bronze cups, respectively, are identical and the teams which drop to a lower league are also identical. How many different possible outcomes are there for the tournament?
I have no idea, is this a question permutations and combinations? As in how can I order (permute) the 6 teams in between the first and last 3? Which I would think would be P(6,6) = 6!
I'm not sure how to order the first and last 3, is it just 6 choose 3 for the first 3, and then 3 choose 3 for the last 3? By multiplication principle: (6 choose 3)*6!