To determine which diagram shows all the possible matches that will be played among the six teams in the sports league, we need to understand that in a league where each team plays every other team exactly once, we can use a combination formula to find the number of matches.
For \( n \) teams, the total number of matches can be calculated using the combination formula:
\[ \text{Matches} = \binom{n}{2} = \frac{n(n-1)}{2} \]
For 6 teams, we substitute \( n = 6 \):
\[ \text{Matches} = \binom{6}{2} = \frac{6 \times 5}{2} = 15 \]
This means there will be a total of 15 matches played.
To visualize the matches, we can consider labeling the teams as A, B, C, D, E, and F. The matches will be as follows:
- A vs B
- A vs C
- A vs D
- A vs E
- A vs F
- B vs C
- B vs D
- B vs E
- B vs F
- C vs D
- C vs E
- C vs F
- D vs E
- D vs F
- E vs F
Now, the task is to identify which of the diagrams (W, X, Y, or Z) represents these matches. Each team should be connected to all other teams in a manner that reflects the total of 15 matches.
Unfortunately, without the actual diagrams provided here, I am unable to identify which option correctly represents the matches. However, you can look for a diagram where each of the 6 teams (A, B, C, D, E, and F) is connected to the other 5 teams, resulting in \( \frac{6 \times 5}{2} = 15 \) edges (matches) in total.
If you have any visual representation of the diagrams, I can help further discuss which one fits the criteria described above.
1 answer