1. The problem statement, all variables and given/known data The NHL currently has a total of 30 teams in 4 divisions (7 teams in the Pacific Division, 7 in the Central Division, 8 in the Metropolitan Division, and 8 in the Atlantic Division). Suppose the NHL gets a new commissioner, and they have the curious notion of reshuffling teams by randomly assigning the 30 teams to the divisions (leaving the number of teams in each division the same as above). How many different ways can this be done? 2. Relevant equations None. 3. The attempt at a solution There are 30 teams and they must be partitioned into teams of 7, 7, 8, 8, which represent the four divisions.. [tex] (30!)/(7!7!8!8!) [/tex] using a partitioning rule.. I'm not sure if this is the right way to go about it, any hints would be appreciated.