Sixteen players `S_1,S_2, ..., S_(16)` play in a tournament. They are divided into eight pairs at random. From each pair a winner is decided on the basis of a game played between the two players of the pair. Assume that all the players are of equal strength.Find the probability that the player `S_1` is among the eight winners.

Sixteen players P_(1),P_(2),P_(3)….., P_(16) play in tournament. If they grouped into eight pair then the probability that P_(4) and P_(9) are in different groups, is equal to

Sixteen players S_(1) , S_(2) , S_(3) ,…, S_(16) play in a tournament. Number of ways in which they can be grouped into eight pairs so that S_(1) and S_(2) are in different groups, is equal to

In a tennis tournament in which every pair has to play with every other pair,10 players are playing.Find the number of games played.

Eight players P_(1),P_(2),P_(3),............P_(8), play a knock out tourrament.It is known that whenever the players P_(i) and P_(j), play,the player P_(i) will win if i

116 people participated in a knockout tennis tournament. The players are paired up in the first round, the winners of the first round are paired up in the second round and so on till the final is played between two players. If after any round, there is odd number of player , one player is given a bye, i.e. he skips thet round and plays the next round with the winners. The total number of matches played in the tournament is

116 people participated in a knockout tennis tournament. The players are paired up in the first round, the winners of the first round are paired up in the second round, and so on till the final is played between two players. If after any round, there is odd number of players, one player is given a by, i.e. he skips that round and plays the next round with the winners. The total number of matches played in the tournment is

8n players P_(1),P_(2),P_(3)……..P_(8n) play a knock out tournament. It is known that all the players are of equal strength. The tournament is held in 3 where the players are paired at random in each round. If it is given that P_(1) wins in the third round. Find the probability that P_(2) looses in the second round.