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In a university games tournament, 64 students are about to participate in a chess knockout competition. The first round consists of 32 games, with...
In a university games tournament, 64 students are about to participate in a chess knockout competition.
The first round consists of 32 games, with two students per game.
The 32 winners of the first round get to play in the second round, which consists of 16 games, and so on, until an overall winner is declared in the sixth round.
(In the case of a draw on any game, a coin is tossed to determine the winner.)
(a) In how many different ways can the 64 participating students be paired up
on the first round?
(Do not consider the order in which students can be paired up.)
(b) Suppose that the 64 participating players are of equal ability,
[8 marks]
and pairing up is purely random on each round.
Find the probability that Eva and Brett (two of the 64 students)
will get to play each other at some stage during the knockout competition.
