Question: Six distinct numbers are randomly distributed to players numbered 1 through 6. Whenever two players compare their numbers, the one with the higher one is

Six distinct numbers are randomly distributed to players numbered 1 through 6. Whenever two players compare their numbers, the one with the higher one is de- clared the winner. Initially, players 1 and 2 compare their numbers; the winner then compares her number with that of player 3, and so on. Let X denote the number of times player 1 is a winner. Find P(X = i), i = 0,1,2,3,4,5.

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