Well here's what I got so far, maybe someone can finish this up:

For the host slot, there are 7 possibilities. For the first team, there are 20 possibilities:

n = 6; k = 3 --> 6! / 3!3! --> 5 x 4 = 20.

For each one of these possibilities, there's only 1 possibility for the second team.

That would be 7 x 20 = 140.

Now how to work in the requirement. I wrote out all the teams that would work, and I got 12 teams. 12 x 7 is 84, so that's my guess of the answer.

However, OA is 50. So I would like to see someone's correct answer to this problem!