Posted by **Andrew** on Saturday, February 18, 2012 at 7:26pm.

In a sports league of n teams in which each team plays every other team twice, the total number N

of games to be played is given by N = n2 - n. What is the total number of games to be played in a

football league having 17 teams?

- math -
**Cheryl**, Saturday, February 18, 2012 at 7:30pm
n = 17

N= (17*2) - 17

- math -
**Andrew**, Saturday, February 18, 2012 at 7:33pm
Thanks Cheryl :-)

- CORRECTION - math -
**Reiny**, Saturday, February 18, 2012 at 9:05pm
The answer given by Cheryl is incorrect.

The number of 2 element subsets (which the above deals with) is C(n,2)

= n!/ ((n-2)!2! )

= n( n-1)/2

so for a double round-robin, the number of games

= 2* (n(n-1)/2

= n(n-1)

= n^2 - n

so for 17 teams, n=17

N = 17^2 - 17 = 272

looks like Cheryl read your formula as 2n - n

which would have been simply n, thus her answer of 17

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