How many collisions happen (over the entire time, i.e. in the future and in the past together) in a system of n identical billiard balls moving with different speeds in an infinite 1-dimensional billiard?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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How many collisions happen (over the entire time, i.e. in the future and in the past together) in a system of n identical billiard balls moving with different speeds in an infinite 1-dimensional billiard? 

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