I thought it might be useful to post a list of standard probability/counting methods for debate tournaments. I list them in order of rapidity of growth -- the last listed expands most quickly, but they all increase without bound. For all of these, there a n teams at the tournament, and n is an even number.
First: once the teams have been separated into aff and neg pools, how many possible matches are there to consider?
Second: how many possible matches are there at a tournament, period? If you don't consider sides, then there are
possible matches. If you did consider sides (A aff vs. B is counted as different than B aff vs. A), then are twice as many possible matches.
Third: how many ways are there to separate the teams into aff and neg pools?
Fourth: once the teams have been separated into aff and neg pools, how many complete (perfect) pairings are possible?
This is the fastest growing number of all.