In a tournament with five teams,each team plays against every other tam exactly once.Each game is won by one of the playing teams and the wining teams score one point,while the losing team scores zero.Which of the following is not necessarily true?
A. There are at least two teams which at the most two points each.
B. There are a tleast two teams which have at least two points each.
C. There at the most three teams which have at least three points each.
D. There are at the most four teams which have at the most two points each
Total teams= five
Total Games= Factorial(5) 10
Factorial(2)x Factorial(3)
Total of points tally is going to be equal to 10(10 x 1)
Let us take the scenario I as mentioned below:
N/A: Not Applicable as E can't win against anybody since no more matches left.
Option A is correct as there are three teams with at the most 2 points each as depicted in table.
Option B is correct as there are three teams with at least 2 points each as depicted in the table.
Let us take Scenario II as mentioned below:
Option C is correct as there are two teams which have 3 points each.
Let us take another Scenario III as mentioned below:
Option D is not necessarily correct as there are 5 teams with at the most 2 points each.
In this scenario if 'D' would have lost against 'E' then it could have been correct but not necessarily true.
Total Games= Factorial(5) 10
Factorial(2)x Factorial(3)
Total of points tally is going to be equal to 10(10 x 1)
Let us take the scenario I as mentioned below:
| Team | Wins Against(b=no. of wins) | Points(b x 1) |
| A | B,C,D,E | 4 |
| B | C,D,E | 3 |
| C | D,E | 2 |
| D | E | 1 |
| E | N/A | 0 |
N/A: Not Applicable as E can't win against anybody since no more matches left.
Option A is correct as there are three teams with at the most 2 points each as depicted in table.
Option B is correct as there are three teams with at least 2 points each as depicted in the table.
Let us take Scenario II as mentioned below:
| Team | Wins Against(b=no.of wins) | Points(b x 1) |
| A | B,C,D | 3 |
| B | C,D,E | 3 |
| C | D,E | 2 |
| D | E | 1 |
| E | A | 1 |
Option C is correct as there are two teams which have 3 points each.
Let us take another Scenario III as mentioned below:
| Team | Wins Against(b=no. of wins) | Points(b x 1) |
| A | B,C | 2 |
| B | C,D | 2 |
| C | D,E | 2 |
| D | A,E | 2 |
| E | A,B | 2 |
Option D is not necessarily correct as there are 5 teams with at the most 2 points each.
In this scenario if 'D' would have lost against 'E' then it could have been correct but not necessarily true.