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
I did not use the approach used in the book. Instead, I did...
8!/2!(8 - 6)! = 8 x 7/2 = 4 x 7 = 28.
Is this a coincedence?
OG - 121 - seems right ???
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- AleksandrM
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I am not sure what OG is used. Dont have it handy now
Here is what I did
If A,B,C,D,E,F,G,H are the teams
A can play with 7 teams
B can play with 6 teams (subtract the one thats already counted between A & B)
and so on
7+6+5+4+3+2+1 = 28
In other words the Question is asking how many games are possible with 8 teams and 2 teams playing a game. How many ways can we pick 2 out of 8? 8 C 2, which is what you did
Here is what I did
If A,B,C,D,E,F,G,H are the teams
A can play with 7 teams
B can play with 6 teams (subtract the one thats already counted between A & B)
and so on
7+6+5+4+3+2+1 = 28
In other words the Question is asking how many games are possible with 8 teams and 2 teams playing a game. How many ways can we pick 2 out of 8? 8 C 2, which is what you did
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- Brent@GMATPrepNow
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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).AleksandrM 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
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
Cheers,
Brent
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- Scott@TargetTestPrep
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We are given that there are 8 teams in a league and that each game is played by 2 teams. Note that each team does not play itself and the order of pairing each team with its opponent doesn't matter. [For example, the pairing of (Team A vs. Team B) is identical to the pairing of (Team B vs. Team A).] The situation can therefore be solved by finding the number of combinations of 8 items taken 2 at a time, or 8C2:AleksandrM 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
8C2 = 8!/[2!(8 - 2)!] = 8!/(2!6!) = (8 x 7)/(2 x 1) = 56/2 = 28
Answer: C
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