Stanley Cup FinalsDate: 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/ |
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