shortest "cut for finding the no of matches in a tourna

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1 > OG-12-PS-121 -
There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

In this question I did 8C2 which was correct.

2 > Team A, team B, team C, and team D take part in a tournament in which every team plays once with each of its opponents.

what is the total number of matches ?

answer is simple 4c2.


3>15 chess players take part in a tournament. If every player plays twice with each of his opponents, how many games will be played?

why is the answer 15P2 and not 15C something here ?
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by Anurag@Gurome » Wed Jul 06, 2011 12:25 am
bblast wrote:1 > OG-12-PS-121 -
There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

In this question I did 8C2 which was correct.

2 > Team A, team B, team C, and team D take part in a tournament in which every team plays once with each of its opponents.

what is the total number of matches ?

answer is simple 4c2.


3>15 chess players take part in a tournament. If every player plays twice with each of his opponents, how many games will be played?

why is the answer 15P2 and not 15C something here ?
Hope you got the difference.
If not, read on...

If they played once with their opponent, number of games = 15C2
If they played twice with their opponent, number of games = 2*(15C2) = 2*(15!/[(15 - 2)!*2!]) = 15!/(15 - 2)! = 15P2
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by bblast » Wed Jul 06, 2011 12:34 am
perfect anurag, so the 15p2 was here was accidental. if each team plays other exactly thrice then we have the solution :

15C2 * 3. Correct ?
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by Anurag@Gurome » Wed Jul 06, 2011 12:42 am
bblast wrote:perfect anurag, so the 15p2 was here was accidental. if each team plays other exactly thrice then we have the solution :

15C2 * 3. Correct ?
I won't say 'accidental' because it is another way to write 2*(15C2). But yes the answer will of the form (Number of times they play)*(15C2).
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