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19 numbered balls in a box, we pick 5 different balls

Source: Flanders Math Olympiad 2021 p3

December 24, 2022
combinatorics

Problem Statement

There are 1919 balls in a box, numbered 11 through 1919. When we go out get that box without looking five different balls, which number has the largest probability of being the difference between the highest and lowest number drawn? Justify you reply .