if there are n teams in a league and each team plays each other twice in a season, the total number

Algebra
Tutor: None Selected Time limit: 1 Day

word problem

May 10th, 2015

If there are 3 teams, then the possible outcomes are

1 =>  2

1 =>  3

----------

2 => 1

2 =>  3

----------

3 =>  1

3 =>  2

----------

So each team plays 4(=2*(3-1)) games and there are 6(=3*(3-1)) games in total.


If there are 4 teams, then the possible outcomes are

1 =>  2

1 =>  3

1 =>  4

----------

2 =>  1

2 =>  3

2 =>  4

----------

3 =>  1

3 =>  2

3 =>  4

----------

4 =>  1

4 =>  2

4 =>  3

----------


So each team plays 6(=2*(4-1)) games and there are 12(=4*(4-1)) games in total.


and continuing like this

If there are n teams, 

each team will play 2(n - 1) games and

there will be a total of n(n - 1) games played.


May 11th, 2015

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