Cooke County schools have 7 teams playing in a basketball
tournament. How many games will be played if each team
plays 3 games against every other team?
To determine the number of games played, we need to find the number of possible matchups between the 7 teams.
First, we find the number of ways to choose 2 teams out of the 7 teams. This can be calculated using the combination formula, which is given by:
nCk = n! / (k!(n-k)!)
where n is the total number of teams and k is the number of teams chosen.
In this case, n = 7 and k = 2:
7C2 = 7! / (2!(7-2)!)
= (7 * 6 * 5 * 4 * 3 * 2 * 1) / (2 * 1 * 5 * 4 * 3 * 2 * 1)
= 21
Therefore, there are 21 possible matchups between the 7 teams.
Since each team plays 3 games against every other team, we multiply the number of matchups by 3:
21 * 3 = 63
So, a total of 63 games will be played in the tournament.