Official Guide Explanation:
Problem Solving #121




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Solution and Metadata

Question: 121
Page: 169
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Counting Methods > Combinations

Explanation: This is a textbook example of a combinations problem. Essentially, each game is a selection of two teams from the overall group of eight, and each game happens only once. Thus, n = 8 (the population), and k = 2 (the selection for each subgroup). So, use the combinations formula: ((n!)/(k!(n - k)!)) and plug in the relevant values: ((8!)/(2!(8 - 2)!)) = (((8)(7)(6!))/(2!6!)) = (56/2) = 28, choice (C).

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