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?
Thanks Cheryl :-)
n = 17
N= (17*2) - 17
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
To find the total number of games to be played in a football league with 17 teams, you can use the formula N = n^2 - n, where n represents the number of teams.
In this case, n = 17.
Now, substitute the value of n into the formula:
N = 17^2 - 17
Simplifying the equation:
N = 289 - 17
N = 272
Therefore, the total number of games to be played in a 17-team football league is 272.