1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Combinatorics: tennis game with 8 people

  1. May 28, 2016 #1

    Math_QED

    User Avatar
    Homework Helper

    1. The problem statement, all variables and given/known data

    8 friends are playing a tennis game together. How many different doubles games of tennis can they play?

    2. Relevant equations

    Combinations

    3. The attempt at a solution

    Well, I solved this problem by saying: we choose a group 4 people from 8 to play, so order is not important, this is C(8,4). If those 4 people are A,B,C,D, they can play together in 3 different ways: AB/CD; AC/BD; AD/BC, so the solution is: 3C(8,4) = 210.

    I tried doing this in another way, but I suppose I am doublecounting something. This was my approach:

    For one team, we choose 2 people out of 8. For the other team, we choose 2 people out of 6 (since 2 out of 8 players are already taken). So, the answer would be: C(8,2)*C(6,2). Now, I am pretty sure that I have doublecounted, but I don't know exactly what it is I have doublecounted.

    It would be great of someone could help me!
     
  2. jcsd
  3. May 28, 2016 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    You counted (AB play against CD) and (CD play against AB) as separate events.
     
  4. May 28, 2016 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    There are C(8,4) ways of choosing a group of 4 to play doubles; for each such group of 4 there are C(4,2) ways of forming two teams of two.
     
  5. May 28, 2016 #4

    Math_QED

    User Avatar
    Homework Helper

    I still don't get it. Where exactly do I do this?
     
  6. May 28, 2016 #5

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Not quite. That double counts the ways of forming 2 teams of 2.
     
  7. May 28, 2016 #6

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    C(8, 2) includes AB as a team; given AB is the first team, C(6, 2) includes CD as a team.

    C(8,2) includes CD as a team; given CD is the first team,C(6,2) includes AB as a team.
     
  8. May 28, 2016 #7

    Math_QED

    User Avatar
    Homework Helper

    Thanks a lot!
     
  9. May 28, 2016 #8

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    If the group is ABCD we can choose one of the pairs to be AB or AC or AD or BC or BD or CD. Whenever we make such a choice, the remaining two form the other pair.
    Of course, I missed that. If the group is ABCD there are only three pairs that A can belong to, and he/she must belong to some pair.
     
  10. May 29, 2016 #9

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    I agree that 38C4 is probably the intended answer, but it is not in accordance with the rules of doubles tennis. within each pair, there is the question of who serves first (throughout the match) and who receives in the right hand court (for the duration of a set).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Combinatorics: tennis game with 8 people
  1. Combinatorics questions (Replies: 16)

  2. Combinatorics Problem (Replies: 12)

Loading...