To calculate the total number of games that must be scheduled for the season, we can use the combination formula, which is used to find the number of ways to choose a certain number of items from a larger set without regard to the order of selection.
Since each of the eight teams must play against every other team once, we need to calculate the number of combinations of 8 teams taken 2 at a time (since each game involves 2 teams playing against each other).
The combination formula is given by:
C(n, k) = n! / (k! * (n - k)!)
Where:
- n is the total number of items (teams in this case),
- k is the number of items to choose (2 teams for each game),
- n! represents the factorial of n, which is the product of all positive integers up to n.
So, the number of games that must be scheduled for the season is:
C(8, 2) = 8! / (2! * (8 - 2)!)
= (8 * 7) / (2 * 1)
= 28
Therefore, the coordinator must schedule 28 games for the season.
