MathDB

Elbert and Yaiza each draw

10

cards from a

20

-card deck with cards numbered

1,2,3,\dots,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.)

Problem Statement