Official Guide Explanation:
Problem Solving #56

Background

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Solution and Metadata

Question: 56
Page: 69
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Data Interpretation >

Explanation: If you don't know how to do this problem, it's an easy one to guess on: to show the distance between all of those cities, do you think you can do it with 6 table entries or less? However, it's useful to know how the math works in case the answer choices are more carefully chosen next time you see it.

This is essentially a combinations problem. Given a population of six cities, how many pairs of cities can be selected from the population? The combinations formula is ((n!)/(k!(n - k)!)), where n is the population (in this case, 6), and k is the number in each subgroup (in this case, 2). Plugging in:

((n!)/(k!(n - k)!)) = ((6!)/(2!(6 - 2)!)) = ((6(5)(4!))/(2!(4!))) = ((6(5))/2) = 15, choice (A).

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