Enigma 1339: Quarter-final draws
17 March 2014
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From New Scientist #2498, 7th May 2005
Of the 8 fifth round games in this year’s FA cup competition 4 were won and 4 required replays. When the draw for the quarter-finals was made each game matched a team that had won against the winner of a replay.
(1) What as a fraction expressed in its lowest terms was the probability that the draw would produce this outcome?
(2) What was the probability (similarly expressed) that it would produce two games that involved the four teams that had won and two that involved the winners of the four replays?