justin, julie, jamie, matt, ryan, and roland are the six players in a round-robin tennis tournament. each player will play a set against each of the other players. list all the sets that need to be played.
I would list the names vertically.
Justin
Julie
Jamie
Matt
Ryan
Roland.
Now pair up one at a time. For example
Justin/Julie
Justin/Jamie
Justin/Matt
Justin/Ryan
Justin/Roland
Then go to the next one; i.e., Julie.
Omit Julie/Justin because you already have that one.
Julie/Jamie
Julie/Matt
Julie/Ryan
Julie/Roland
etc.
To determine all the sets that need to be played in a round-robin tennis tournament with six players, each player plays a set against each of the other players. Here is a step-by-step breakdown of the matches:
Step 1: Justin plays against Julie, Jamie, Matt, Ryan, and Roland.
Step 2: Julie plays against Jamie, Matt, Ryan, and Roland.
Step 3: Jamie plays against Matt, Ryan, and Roland.
Step 4: Matt plays against Ryan and Roland.
Step 5: Ryan plays against Roland.
Combining all the matches from steps 1 to 5, the sets that need to be played are:
1. Justin vs. Julie
2. Justin vs. Jamie
3. Justin vs. Matt
4. Justin vs. Ryan
5. Justin vs. Roland
6. Julie vs. Jamie
7. Julie vs. Matt
8. Julie vs. Ryan
9. Julie vs. Roland
10. Jamie vs. Matt
11. Jamie vs. Ryan
12. Jamie vs. Roland
13. Matt vs. Ryan
14. Matt vs. Roland
15. Ryan vs. Roland
So, a total of 15 sets need to be played in the round-robin tennis tournament.
To determine the sets that need to be played in a round-robin tennis tournament with six players, you need to know that each player will play against every other player once.
To generate the list of sets, you can use the formula for the number of combinations without repetition, which is calculated as n choose 2. In this case, n represents the total number of players, which is 6.
Using the formula, you can calculate the number of sets as follows:
6 choose 2 = (6!)/((2!)(6-2)!) = (6 x 5) / (2 x 1) = 15
So, there will be a total of 15 sets that need to be played in this round-robin tournament.
To get the list of sets, you can pair up each player against every other player once. Here is the list of all the sets that need to be played:
1. Justin vs. Julie
2. Justin vs. Jamie
3. Justin vs. Matt
4. Justin vs. Ryan
5. Justin vs. Roland
6. Julie vs. Jamie
7. Julie vs. Matt
8. Julie vs. Ryan
9. Julie vs. Roland
10. Jamie vs. Matt
11. Jamie vs. Ryan
12. Jamie vs. Roland
13. Matt vs. Ryan
14. Matt vs. Roland
15. Ryan vs. Roland
Each of these sets represents a match between two players.