How many possible sequences of tennis matches with 6 players over 4 weeks?

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The discussion centers on calculating the number of possible sequences of tennis matches involving 6 players over 4 weeks, where each week features a different pair of players. The key calculation involves determining the number of combinations of pairs, specifically using the formula 6C2 for pairs, resulting in 15 possible pairs. The sequences of matches are calculated using permutations, leading to 15P4 for the total sequences of matches. The conversation also explores variations of the problem, such as excluding players from the matches.

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There are 6 tennis players and each week for a month (4 weeks) a different pair of 5 play a tennis match. How many ways are there to form the sequence of 4 matches so that every player plays at least once?

I believe this is an OR problem, but I don't know how to handle the 4 weeks information and how do you count this?

thanks
 
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The 4 weeks just refers to the 4 matches. Since there are 6 players there are 6C2 = 15 pairs. Now with 4 matches there are 15P4 possible sequences (since sequences means that the order matters). If we wanted to exclude one person we would have 5C2 pairs and (5C2)P4 possible sequences. What if we tried to exclude two people? Can you go from here?

-Dale
 

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