Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A tournament includes P total players. The game played in rounds with teams of size T. Possible number of teams is (P T).

Questions

  • How would you calculate the number of total possible combinations of matches?
  • How would you calculate the number of total possible matches per round?

Examples

Example 1: 4 players in teams of 2
4 Players
1-2
1-3
1-4
2-3
2-4
3-4
=(4 2) = 6

1-2 - 3-4
1-3 - 2-4
1-4 - 2-3
= 3


Example2: 5 players in teams of 2
Teams
1-2
1-3
1-4
1-5
2-3
2-4
2-5
3-4
3-5
4-5
=(5 2) = 10

Matches
1-2 - 3-4
1-2 - 3-5
1-2 - 4-5
1-3 - 2-4
1-3 - 2-5
1-3 - 4-5
1-4 - 2-3
1-4 - 2-5
1-4 - 3-5
1-5 - 2-3
1-5 - 2-4
1-5 - 3-4
2-3 - 4-5
2-4 - 3-5
2-5 - 3-4
= 15
share|improve this question

1 Answer 1

up vote 1 down vote accepted

you have to chose the first and the second teams. for the first team you have $\binom{P}T$ and for the second team you have $\binom{P-T}T$ however you are counting each match twice in this case so the total number of possible matches is $$\frac{\binom{P}T\binom{P-T}T}{2}$$

The number of possible combinations of matches per round (assuming you get as many teams to play as possible in each round) is $$\prod_{n=0}^{n=2\lfloor{T/2P}\rfloor-1}\binom{P-(Tn)}T/(\lfloor{T/2P}\rfloor!(2^{\lfloor{T/2P}\rfloor})$$

share|improve this answer
    
Thank you very much! –  nkadwa Jan 11 '13 at 15:30

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.