A tournament has 16 teams. How many ways are there to match up the teams in 8 pairs? Is it (16 choose 2)(14 choose 2)(12 choose 2)(10 choose 2)(8 choose 2)(6 choose 2)(4 choose 2)(2 choose 2)?
2026-03-27 02:35:22.1774578922
Counting the number of possible matchups for teams
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No, it's not. It is only 15*13*...*1, or 15!!
We consider one of the teams. It has 15 choices for its partner Then consider another of the remaining 14 teams. It has 13 choices Continue doing this, until we only get 1 choice
so the answer is 15*13*...*1=15!!.