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
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.