Permutation for first round

2n players are participating in a tennis tournament. Find the number Permutation of pairings for the first round

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2305
Shaswata Roy ·

We choose the first player.Now he can be paired with any of the remaining 2n-1 players.
Now we chose the second player.He can be paired with any of the remaining 2n-3 players.
Next we chose the third player.He can be paired with any of the remaining 2n-5 players.
....
Continuing this n times we get the total number of permutations to be = (2n-1)*(2n-3)*(2n-5)....3*1
which is = (2n)!2nn!

  • Hardik Sheth you can also justify as-first find total no of permutations....remove overcalculation due to n teams as none is special...remove overcalculation due to 2 players within a team for n teams...

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