# math

posted by .

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 -

n = 17
N= (17*2) - 17

• math -

Thanks Cheryl :-)

• CORRECTION - math -

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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