The number of teams and matches in the soccer league illustrates permutation and combination
There are 12 teams in the soccer league in the first season
The number of teams in the soccer league is given as n.
So, the total number of matches played in a season is:
Matches = n(n-1)/2
When the number of teams increases by 2, we have:
Matches = (n + 2)(n + 2 -1)/2
Also, the number of matches increases by 27.5%.
So, we have:
Matches = n(n-1)/2 * (1 + 27.5%)
Equate both equations
[tex]\frac{(n + 2)(n + 2 -1)}{2} = \frac{n(n-1)}{2} * (1 + 27.5\%)[/tex]
Simplify
[tex]\frac{(n + 2)(n + 1)}{2} = \frac{n(n-1)}{2} * (1.275)[/tex]
Multiply through by 2
[tex](n + 2)(n + 1) = n(n-1) * (1.275)[/tex]
Expand
[tex]n^2 + 3n + 2 = 1.275n^2 - 1.275[/tex]
Collect like terms
[tex]n^2 -1.275n^2+ 3n + 2 +1.275 = 0[/tex]
Evaluate the like terms
[tex]-0.275n^2+ 3n + 3.275 = 0[/tex]
Using a graphing calculator, we have:
n = -1 or n = 11.909
n cannot be negative.
So, we have:
n = 11.909
Approximate
n = 12
Hence, there are 12 teams in the soccer league in the first season
Read more about permutation and combination at:
https://brainly.com/question/12468032
