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Homework Help: Combinatorics problem

  1. Dec 18, 2005 #1
    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?

  2. jcsd
  3. Dec 19, 2005 #2


    Staff: Mentor

    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?

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