In a twelve-team bowling league, if every team plays every other team four times during the season. How many games must be scheduled?
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I do not know. The only reason I came here is because I thought someone had the answer.
To determine the number of games that need to be scheduled, we need to calculate the total number of games played between all teams.
In a twelve-team bowling league, every team will play against every other team. Since each team plays four times against every other team, we can calculate the number of games between two teams as follows:
Number of games between two teams = 4
Since there are 12 teams in total, we need to calculate the number of games between all possible pairs of teams.
To do this, we can use the combination formula, which is nCr = n! / (r! * (n-r)!), where n is the total number of teams and r is the number of teams playing against each other.
In this case, n = 12 and r = 2 (since we are considering pairs of teams). Plugging these values into the combination formula:
Number of games between all pairs of teams = 12C2 = 12! / (2! * (12-2)!).
Calculating this:
Number of games between all pairs of teams = (12 * 11) / (2 * 1) = 66.
Therefore, 66 games must be scheduled in a twelve-team bowling league, where every team plays every other team four times during the season.