8 players compete in a tournament, everyone plays everyone else just once. The winner of a game gets 1, the loser 0 or each gets 1/2 if the game is drawn. The final result is that every one gets a different score and the player placed at second gets the same score as the total of four bottom players.

A, B, C D, ..................X, Y, Z are the players who participated in a tournament. Everyone played with every other player exactly once. A win scores 2 points, a draw scores 1 point and a loss scores 0 points. None of the matches ended in a draw. No two players scored the same score. At the end of the tournament, the ranking list is published which is in accordance with the alphabetical order. Then

In each of a set of games it is 2 to 1 in favour of the winner of the previous game. The chance that the player who wins the first game shall win three at least of the next four is

Three players play a total of 9 games.In each game,one person wins and the other two lose; the winner gets 2 points and the losers get -1 each.The number of ways in which they can play all the 9games and finish each with a zero score is

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 decided to the basis of a game played between the two players of the pair. Assume that all the players are of equal strength. (a) Find the prabability that the player S_(1) is among the eight winners. (b) Find the probability that exactly one of the two players S_(1)and S_(2) is among the eight winners.

In each of a set of games it is 2 to 1 in favor of the winner of the previous game: what is the chance that the player who wins the first game shall win three at least of the next four.

Study the given information carefully and answer the following questions. There was a football tournament of three teams i.e. A, B and C in which each team played 2 matches. Score pattern of the tournament is: • A team gets 2 points for scoring a goal against the opponent team. • A team gets 3 points for scoring a goal against the opponent team from the outside area. • There is a penalty of 1 point if a team concedes a goal. • Only three players from each team scored the goals. A – B Match: B is the winner of this game. Total points scored by B in this match is 4 . Also, team A scored 2 goals and none of the players scored the goal from the outside area. A – C Match: C scored 0 points in the match. Only one player from team A scored a goal from outside area. A scored 4 points in this match. B – C Match: B gets 6 points from match. Team C scored 1 goal more than Team B. One player from team B scored a goal from outside area but none from team C. The given 3 teams are ranked on the basis of total marks in such a way that the highest scoring team is ranked 1, the second highest scoring team is ranked 2 and the least scoring team is ranked 3. Rank 3 got a total of Rs. 60,000 as prize money. If the ratio of the prize money of the rank 1, rank 2 and rank 3 team is 8 : 5 : 3, which of the following combinations of team and prize money is correct?