2014 AMC 8

Complete problem set with solutions and individual problem pages

Problem 16 Hard

The "Middle School Eight" basketball conference has 8 teams. Every season, each team plays every other conference team twice (home and away), and each team also plays 4 games against non-conference opponents. What is the total number of games in a season involving the "Middle School Eight" teams?

  • A.

    60

  • B.

    88

  • C.

    96

  • D.

    144

  • E.

    160

Answer:B

Within the conference, there are 8 teams, so there are \dbinom{8}{2}=28 pairings of teams, and each pair must play two games, for a total of 28\cdot 2=56 games within the conference.

Each team also plays 4 games outside the conference, and there are 8 teams, so there are a total of 4\cdot 8 =32 games outside the conference.

Therefore, the total number of games is 56 + 32 = \boxed{\text{(B) }88}.

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