MathDB
Problems
Contests
National and Regional Contests
Portugal Contests
Portugal MO
2022 Portugal MO
5
5
Part of
2022 Portugal MO
Problems
(1)
10 professionals and 6 amateurs in a badminton competition
Source: Portugal OPM 2022 p5
5/15/2024
In a badminton competition,
16
16
16
players participate, of which
10
10
10
are professionals and
6
6
6
are amateurs. In the first phase, eight games are drawn. Among the eight winners of these games, four games are drawn. The four winners qualify for the semi-finals of the competition. Assuming that, whenever a professional player and an amateur play each other, the professional wins the game, what is the probability that an amateur player will reach the semi-finals of the competition?
combinatorics