3

Part of 2021 Flanders Math Olympiad

Problems(1)

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

Source: Flanders Math Olympiad 2021 p3

19

balls in a box, numbered

1

19

. 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 .