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Omni-MATH / Elbert and Yaiza each draw 10 cards from a 20-card deck with cards numbered…

Problem

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problem

Elbert and Yaiza each draw 10 cards from a 20-card deck with cards numbered 1,2,3,…,201,2,3, \ldots, 20. Then, starting with the player with the card numbered 1, the players take turns placing down the lowest-numbered card from their hand that is greater than every card previously placed. When a player cannot place a card, they lose and the game ends. Given that Yaiza lost and 5 cards were placed in total, compute the number of ways the cards could have been initially distributed. (The order of cards in a player's hand does not matter.)
Plain-text mathematical notation (without MathML)
Elbert and Yaiza each draw 10 cards from a 20-card deck with cards numbered 1,2,3,…,20. Then, starting with the player with the card numbered 1, the players take turns placing down the lowest-numbered card from their hand that is greater than every card previously placed. When a player cannot place a card, they lose and the game ends. Given that Yaiza lost and 5 cards were placed in total, compute the number of ways the cards could have been initially distributed. (The order of cards in a player's hand does not matter.)
Original LaTeX notation
Elbert and Yaiza each draw 10 cards from a 20-card deck with cards numbered $1,2,3, \ldots, 20$. Then, starting with the player with the card numbered 1, the players take turns placing down the lowest-numbered card from their hand that is greater than every card previously placed. When a player cannot place a card, they lose and the game ends. Given that Yaiza lost and 5 cards were placed in total, compute the number of ways the cards could have been initially distributed. (The order of cards in a player's hand does not matter.)

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Source and history

task_id
75446783-581e-568f-837f-70e0b67f158d
task_key
test--75446783-581e-568f-837f-70e0b67f158d
task_revision_id
1
config / split
/ test

Official source

initial import