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There are 8 teams in a certain league and each team plays ea
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31 Aug 2020, 10:37
31 Aug 2020, 10:37
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There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?
A. 15
B. 16
C. 28
D. 56
E. 64
A. 15
B. 16
C. 28
D. 56
E. 64
Re: There are 8 teams in a certain league and each team plays ea
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31 Aug 2020, 10:37
31 Aug 2020, 10:37
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
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Re: There are 8 teams in a certain league and each team plays ea
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31 Aug 2020, 10:58
31 Aug 2020, 10:58
1
Carcass wrote:
There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?
A. 15
B. 16
C. 28
D. 56
E. 64
A. 15
B. 16
C. 28
D. 56
E. 64
APPROACH #1: Number sense
There are 8 teams. If we ask each team, "How many teams did you play?" we'll find that each team played 7 teams, which gives us a total of 56 games (since 8 x 7 = 56).
From here we need to recognize that each game has been COUNTED TWICE.
For example, if Team A and Team B play a game, then Team A counts it as a game, and Team B ALSO counts it as a game.
So, to account for the DUPLICATION, we'll divide 56 by 2 to get 28
Answer: C
APPROACH #2: Combinations
Since the order in which we select two teams to play does not matter, we can use combinations
We can select 2 teams from 8 teams in 8C2 ways
8C2 = 28
To learn how to quickly calculate combinations (like 8C2), watch the video below.
Answer: C
Cheers,
Brent
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