SOLUTION: Twelve hockey players are going to be divided into two teams of six in such a way that the two best players are on opposite teams. In how many ways can this be done?

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Question 136401: Twelve hockey players are going to be divided into two teams of six in such a way that the two best players are on opposite teams. In how many ways can this be done?
Answer by stanbon(75887) About Me  (Show Source):
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Twelve hockey players are going to be divided into two teams of six in such a way that the two best players are on opposite teams. In how many ways can this be done?
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Place the two best players: 2 ways
Pick 5 for one of the teams: 10C2 = 45 ways
The remaining plays go on the other team: 1 way
But the two groups of 5 could be swithced: 2 ways
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Total #of ways 2*45*1*2 = 180 ways
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Cheers,
Stan H.