SOLUTION: If 2n teams are to be assigned to play in 1, 2, 3, .... n games in the first round of a bracket, how many ways can the teams be assigned to the games?
thanks
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-> SOLUTION: If 2n teams are to be assigned to play in 1, 2, 3, .... n games in the first round of a bracket, how many ways can the teams be assigned to the games?
thanks
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Question 351011: If 2n teams are to be assigned to play in 1, 2, 3, .... n games in the first round of a bracket, how many ways can the teams be assigned to the games?
thanks Answer by sudhanshu_kmr(1152) (Show Source):
You can put this solution on YOUR website! there are 2n teams and n games, each game have 2 team...
for first match team can be assigned by 2nC2 ways
now there are only (2n -2) team
for second game team can be assigned by (2n-2)C2 ways
for third game ....................... (2n-4)C2 ways
for fourth game .................... (2n-6)C2 ways
and so on.
total no. of ways = 2nC2 * (2n-2)C2 * ..............* 4C2 * 2C2
after solving it we will find (2n)! / (2*2*2...n times)
= (2n)! / (2^n)
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