I am a DOTA 2 player and I came across this intriguing problem which I do not know how to solve. In this game 1 match is played between two teams, each consisting of 5 players. Each player has to pick a hero/character from a pool of total 107 heroes, i.e 10 heroes picked. Moreover both team's captain bans 5 heroes for other team to pick. i.e 10 heroes banned.
Now, in a tournament of 16 teams, played on a knockout format with each contest between two teams consisting of 3 matches (best of 3 winner) and grand final of 5 matches. What is the probability that atleast X (lets say 5) heroes will not be picked or banned in whole tournament.