Current Puzzle

Candy Collectors

Five children went trick-or-treating together and decided to randomly split their candy haul at the end of the night.  As it turned out, they got a total of 25 pieces of candy, 5 copies each of 5 different types (they live in a small town).  They distribute the candies by choosing an ordering of the 25 uniformly at random from all shufflings, and then giving the first 5 to the first child, the second 5 to the second, and so on.

What is the probability that each child has one type of candy that they have strictly more of than every other trick-or-treater? Give your (exact!) answer in a lowest terms fraction.

November update: correct solutions to this puzzle have come in more slowly than others, so we are going to keep it up for an extra month and will have a new puzzle on the site in early December.

Correct Submissions as of 17/11/20

Guillermo Wildschut
Rahul Saxena
Harrison W
Kilian B.
Mrs Nesbitt
Glauber Guarinello
Dimas Ramos
Keith Schneider
Alex Lang
Carl Placid
Conor Mac Amhlaoibh
Sébastien Geeraert
Konstantin Vladimirov
Jonah Goldstein
Walter Sebastian Gisler
Senthil Rajasekaran
Will C
Ben Reiniger
Neil Thistlethwaite
Konstantin Gukov
Alen Abdrakhmanov
Sergey Serebryakov
Rishabh Vaid
Yongxing Wang
Karl Mahlburg
Leif Metcalf
Maria Kormacheva
Edward Wall
Ian Sleightholme
Calvin Pozderac
Alex Kalbach
Will Liao
David Molay
Nikolay Zakharov
Tomer Tzadok
Michael Ore
Kelvin Davis
Andrew Argatkiny
Henry Heffan
Sergey Tychinin
Stefan Glock
Martin Hesselborn
Lazar Ilic
Aleksandar Bukva
Janko Sustersic
Sean Egan
Iman Hosseini
Jordi G Rodríguez

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