. A small monster athletic tournament has n teams, ranked 1 to n. In the first match, the nth ranked team plays the (n - 1)th ranked team. The loser of that natch finishes in last place. The winner of the first match plays the (n- 2)th anked team. The loser of that match finishes in second to last place. The winner of the second match goes on to play the (n-3)th ranked team, and so on. The last match will pit the previous match winner against the first-ranked team. The winner of

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5. A small monster athletic tournament has n teams, ranked 1 ton.
• In the first match, the nth ranked team plays the (n - 1)th ranked team. The loser of that
match finishes in last place.
• The winner of the first match plays the (n - 2)th
ranked team. The loser of that match finishes in second to last place.
• The winner of the second match goes on to play the (n - 3)th ranked team, and so on.
• The last match will pit the previous match winner against the first-ranked team. The winner of
this last match wins the tournament, and the loser of this last match places second in the
tournament.
In how many different orders can the n teams finish?
Notes:
• Count two orders as different if at least one team receives a different finishing position in the
two orders.
• As a quick example, in a tournament with three teams A, B and C, with A ranked first, B
ranked second and C ranked third, here are the following four possible finishing orders: (A, B,
C), (А, С,В), (В, А, С) and (C, A, B).
• Note that in this example, A can't finish worse than second place, since A only plays in the last
match and is guaranteed to be first or second!
Transcribed Image Text:5. A small monster athletic tournament has n teams, ranked 1 ton. • In the first match, the nth ranked team plays the (n - 1)th ranked team. The loser of that match finishes in last place. • The winner of the first match plays the (n - 2)th ranked team. The loser of that match finishes in second to last place. • The winner of the second match goes on to play the (n - 3)th ranked team, and so on. • The last match will pit the previous match winner against the first-ranked team. The winner of this last match wins the tournament, and the loser of this last match places second in the tournament. In how many different orders can the n teams finish? Notes: • Count two orders as different if at least one team receives a different finishing position in the two orders. • As a quick example, in a tournament with three teams A, B and C, with A ranked first, B ranked second and C ranked third, here are the following four possible finishing orders: (A, B, C), (А, С,В), (В, А, С) and (C, A, B). • Note that in this example, A can't finish worse than second place, since A only plays in the last match and is guaranteed to be first or second!
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