In the Eastern Conference of the National Basketball Association (NBA), the Atlantic, Southeast, and Central Divisions have five teams each. During the regular season, each team plays every other team in its own division four times a year, plays six of the teams from the other two divisions four times a year, plays the remaining four teams from the other two divisions three times a year, and plays each team in the Western conference (which has 15 teams) twice. How many games are played by a team in the Eastern Conference during the regular season?
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Each team in the Atlantic, Southeast, and Central Divisions plays 4 games against the other 4 teams in its division, which equals 4 x 4 = 16 games within their own division.
Next, each team plays 6 of the teams from the other two divisions 4 times a year, which equals 6 x 4 = 24 games against teams from the other two divisions.
Each team then plays the remaining 4 teams from the other two divisions 3 times a year, which equals 4 x 3 = 12 games against those teams.
Each team also plays each team in the Western conference, which has 15 teams, twice a year for a total of 15 x 2 = 30 games against Western conference teams.
Adding up all these games, we have:
16 games within own division + 24 games against other two divisions + 12 games against remaining teams in other divisions + 30 games against Western conference teams = 16 + 24 + 12 + 30 = 82 games played by a team in the Eastern Conference during the regular season.