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Tennis Match Winners

Date: 07/18/2003 at 00:44:21
From: Geoff
Subject: Tennis matches

There are 7 tennis matches this weekend, of which there can only be a 
win or loss in each match.

How do I explain to my son the following: How many different 
combinations of winners can there be?

Can a table be drawn to show the possible combination of winners?

Many thanks--hope you can help.


Date: 07/18/2003 at 12:04:30
From: Doctor Douglas
Subject: Re: Tennis matches

Hi Geoff,

Thanks for writing to the Math Forum.

You have to make 7 choices - a winner for the first match, a winner
for the second, etc.

Hence there are a total of 

  2 x 2 x 2 x 2 x 2 x 2 x 2 = 2^7 = 128 

possible winners. You could draw a table, but perhaps more useful
would be a tree.  

                         *                 in match 1, A v. B
                       /   \
                      A     B              either A or B wins
                     / \   / \             in match 2, C v. D
                   AC  AD BC  BD           either C or D wins,
                                             4 possible winner sets
                        
                                           in match 3, E v. F
          ACE ACF ADE ADF BCE BCF BDE BDF    8 possible winner sets

                                           in match 4, G v. H
                                             16 sets
  ACEG ACEH ACFG ACFH ADEG ADEH ADFG ADFH
    BCEG BCEH BCFG BCFH BDEG BDEH BDFG BDFH

and so on, for the remaining three matches.

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/ 


Date: 07/19/2003 at 02:30:45
From: Geoff
Subject: Thank you (Tennis matches)

Thank you very much we know understand the principle.

Have a great day.
Geoff
Associated Topics:
High School Permutations and Combinations

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