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)

Monjur Alahi

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
A. `((14)!)/(2^(6)*6!)`
B. `((15)!)/(2^(7)*7!)`
C. `((14)!)/(2^(7)*6!)`
D. `((14)!)/(2^(6)*7!)`


0 like 0 dislike
1 views
Share with your friends

1 Answers

Salim Ahmed Kawsar

Call

Correct Answer - A
`(a)` Required number of ways
`=("Number of ways in which" 16 "players can be divided in" `8` "couples")-("Number of ways when" S_(1) "and" S_(2) "are in the same group")`
`=(16!)/(2^(8)*8!)-((14)!)/(2^(7)*7!)=(16*15*14!)/(2*2^(7)*8*7!)-((14)!)/(2^(7)*7!)`
`=((14!))/(2^(7)*7!)[(16*15)/(16)-1]=((14)*(14)!)/(14*(6!)*2^(6))=((14!))/(2^(6)*6!)`

0 like 0 dislike
1 views
Talk Doctor Online in Bissoy App
`2^n` players of equal strength are playing a knock out tournament. If they are paired at randomly in all rounds, find out the probability that out of

Four players will reach in semi-final. Since all the players are of equal strength, this is equivalent to selecting four players out of `2^(n)` players. Total number of ways =...

2 Answers 1 views
Eight players `P_1, P_2, P_3, ...........P_8`, play a knock out tournament. It is known that whenever the players `P_i and P_j`, play, the player `P_i

`P_(1) P_(2) P_(3) P_(4) P_(5) P_(6) P_(7) P_(8)` Given that if `P_(i), P_(j)` play with `i lt j`, then `P_(i)` will win. For the first round, `P_(4)` should be paired...

2 Answers 1 views
In a knockout tournament `2^(n)` equally skilled players, `S_(1),S_(2),….S_(2n),` are participatingl. In each round, players are divided in pair at ra

Given `S_(2)` reaches the semi-finals. Since all other players `(2^(n) - 1)` are equally likely to win the finals with probability p. `therefore (2^(n)-1)p+(1)/(4) = 1` `(2^(n) - 1)p =...

2 Answers 1 views
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 strngth. The tournat random is h

Let A be the event of `P_(1)` winning in third round and B be the event of `P_(2)` winning in first round but ossing in second round. We have `P(A)(""^(8n-1)C_(n-1))/(""^(8n)C_(n))=1/8`...

2 Answers 1 views
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 ba

(a) The probability of `S_(1)` to be among the eight winners is equal to the probability of `S_(1)` winning in the group, which is given by 1/2. (b) If `S_(1)...

2 Answers 1 views
Thirty two players ranked 1 to 32 are playing is a knockout tournament. Assume that in every match between any two players, the better ranked player w

Correct Answer - A For ranked 1 and 2 players to be winners and runners up respectively, they should not be paired with each other in any round. Therefore, the required...

2 Answers 3 views
Thirty-two players ranked 1 to 32 are playing in a knockout tournament. Assume that in every match between any two players the better ranked player wi

Correct Answer - 3 For ranked 1 and 2 players to be winners and runners up, respectively, they should not be paired with each other in any round. `impliesp=30/31xx14/15xx6/7xx2/3=16/31`

2 Answers 2 views
`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

Correct Answer - A `(a)` Since one player emerges the winner, each of the remaining `115` players loses in some round. So `115` matches are played. Alternatively , `58+29+14+7+4+2+1=115`

2 Answers 1 views
The number of ways of arranging `6` players to throw the cricket ball so that oldest player may not throw first is

Correct Answer - B `(b)` For the first place `5` players (excluding the oldest) and for the remaining place `5` (including the oldest)players are available. `:.` No of ways `=5xx5xx4xx3xx2xx1=600`

2 Answers 1 views
There are `12` pairs of shoes in a box. Then the possible number of ways of picking `7` shoes so that there are exactly two pairs of shoes are

Correct Answer - A `(a)` Selecting any two pairs, number of ways `=.^(12)C_(2)` Now we have to select remaining three shoes from `10` pairs such that no pair is selected. Three...

2 Answers 1 views
X