Guided Example #1 - Factorials, Combination, Permutation

When the teams play each other, order does not matter, we are counting match ups.  For each game there is a group of two teams playing.  So we can use combinations to help us out here.
Note that if we were putting these teams in any kind of order, then we would need to use permutations to solve the problem.
But in this case, order does not matter, so we are going to use combinations.

First we need to find n and r :
 
${\displaystyle n=9,r=2}$

Let's put those values into the combination formula and see what we get:
${\displaystyle C_r^n=n\frac{!}{r!(n-r)!}}$ Evaluate inside ( )
${\displaystyle C_2^9=9\frac{!}{2!(9-2)!}}$

Expand 9! Until gets to 7! ${\displaystyle C_2^9=\frac{9.8.7!}{2}!7!}$

*Cancel out 7!'s ${\displaystyle C_r^n=\frac{9.8}{2}\ne 36}$