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?
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.