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math

posted by on .

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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