How Many Ways Can A Team Win A 7-Game Series?

SCORE Mathematics

Standards Connections

How Many Ways Can A Team
Win A 7-Game Series?

Introduction: Students will discover how many ways a team can win a 7-game series (NBA Finals, World Series, Stanley Cup) by accessing the Internet and then systematically constructing a sample space which lists all the possible ways.

Prior Knowledge: Basic introduction to sample spaces.

Grade Level: 8-12

Task: Students will systematically construct a sample space listing all the ways a team can win a 7-game series. For example, in the 1996 NBA Finals, the Bulls beat the Sonics by winning the first three games, losing the next two, and then winning game six (Win-Win-Win-Loss-Loss-Win or WWWLLW) How many other ways are there?

Resources:

1996 NBA Playoffs
http://www.infoplease.lycos.com/ipsa/A0003695.html

NBA Finals 1997
http://www.nba.com/history/playoffs/19961997.html

1998 Playoffs - NBA Finals Recaps
http://www.nba.com/history/finals/19971998.html

1997 World Series
http://mlb.mlb.com/NASApp/mlb/mlb/history/postseason/mlb_ws_recaps.jsp?feature=1997

1998 World Series
http://www.cnnsi.com/baseball/mlb/1998/postseason/

1999 World Series
http://www.cnnsi.com/baseball/mlb/1999/postseason/world_series/

Major League Baseball - World Series Archives
http://mlb.mlb.com/NASApp/mlb/mlb/history/postseason/mlb_ws.jsp?feature=recaps_index

Process:
1. Students will access the Internet address above and list the examples of winning a 7-game series. For example, in 1996, the following occurred:

a) WWWLLW (Win-Win-Win-Loss-Loss-Win)
b) WWWW
c) WWLWLLW
d) WWLWW
e) WWWLW
f) WWWW
g) WLWWLW

Then have the students determine if these are all the possible ways.

2. Have the students consider a 5-game series. Model systematically constructing a sample space by creating or having the students help you create the following for all to see:

Win 3-0
WWW

Win 3-1
LWWW
WLWW
WWLW

Win 3-2
LLWWW
LWLWW
LWWLW
WLLWW
WLWLW
WWLLW

These are the only 10 ways to win a 5-game series. Note the position of the losses. Note that a series never ends with an L. (A series can't be won by losing the final game)

3. Have each individual student systematically construct a sample space on paper listing all the possible ways a team can win a 7-game series. A teacher might want to mention there are 35 possible ways. Or maybe a teacher would rather leave it more open-ended.

Learning Advice: Some students may need to study the nature of a 3-game series before working with a 5-game series or a 7-game series.

Evaluation: If this activity is done near the end of a unit which contained many examples of constructing sample spaces, individuals could be graded on an objective basis (example: 90% correct=A, 80% correct=B, etc.). If this activity is done at the start of a unit, a teacher might want to have groups of students work together and try to list as many ways as possible.

Extensions: Pascal's Triangle Combinations and Permutations

Conclusion: Students who successfully construct a sample space listing all the possible ways will have solved a real-life problem as well as improving their skills in probability and mathematical reasoning.

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California Mathematical Academic Standards:

Grade 8-12:
Algebra II #18
18.0 Students use fundamental counting principles to compute combinations and permutations.

NCTM 9-12: Mathematics as Problem Solving; Mathematics as Reasoning; Mathematical Connections; Probability.