# probability

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## probability

 P1, P2, . . . , P8 are eight players participating in a tournament. If i < j, then Pi will win the match against Pj. Players are paired up randomly for first round and winners of this round again paired up for the second round and so on. Find the probability that P4 reaches in the final. How to get the answer??? Guys, answer is coming 4/35.
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## Re: probability

 Is answer correct.. I am getting 4/35*1/3 may b some mistake.. please check it.. players are .. 1,2,3,4,5,6,7,8 final round will be third round... so, player 1 has to win 1st and second round.. this required that in both rounds he is paired with one of (5,6,7,8) and therefore, also that ..one of these shud also reach second round.. so that 4 can be paired with that.... for first round.. probability of such pairing = 4/7* 3C2/6C2.. (4/7 for P4 getting paired with 5,6,7,8 out of all 7...and second part cuz we want a pair from 5,6,7,8 as well..so that winner reaches second round where P4 can defeat it) ... this comes out to be 4/35... now in second round.. we have total 4 ppl.... Player 4.. someone from (5,6,7,8) and two players from (1,2,3) ... for reaching finals he needs to get paired with some1 frm (5,6,7,8) .... and probability of that is.. 1/3 ... so my answer become 4/35*1/3 .. Thats what I got! :/