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Stanley Cup Finals


Date: 10/26/1999 at 20:20:50
From: Pascal Cote-Julien
Subject: Permutations and Combinations

Here is the question I have trouble answering:

In a Stanley Cup final, team A and team B play until one team wins 4 
games. The sequence of game winners is designated by letter; for 
example, ABBBB means team A won the first game and team B won the next 
four games. How many different Stanley Cup finals are possible?

If you could I help me I would be very grateful.

Thanks,
Pascal


Date: 10/27/1999 at 07:43:03
From: Doctor Anthony
Subject: Re: Permutations and Combinations

The number of ways with B winning is shown in the table.

    Combinations          Number of Sequences
    ------------------------------------------
     BBB|B                           1
    ABBB|B              4!/[1!3!] =  4
   AABBB|B              5!/[2!3!] = 10
  AAABBB|B              6!/[3!3!] = 20
                       ------------------
                           Total  = 35

and we get a further 35 possible sequences with A winning, so the 
total number of sequences is  35 + 35 = 70

There are 70 possible sequences for the Stanley Cup finals.

- Doctor Anthony, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Permutations and Combinations

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