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OG12: There are 8 teams in a certain league

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OG12: There are 8 teams in a certain league

by nhai2003 » Sun Sep 13, 2009 1:45 am
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

Guys, please help me with this one. I have difficulty in undertanding the wording of this problem.

Thanks!
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by Nermal » Sun Sep 13, 2009 1:59 am
IMO C (28)

You have 8 teams (A,B,C,D,E,F,G,H) that play against one another.
A vs. B
A vs. C
A vs. D
A vs. E
A vs. F
A vs. G
A vs. H

Since no team can play against itself, A plays 7 games.
B plays also 7 games, but now we have counted the game A vs. B and B vs. A which is the same.
Therefore we must substract this game once.
You can do this with all combinations and you end up with: 7+6+5+4+3+2+1=28

It seems to take quite some time, but actually it doesn't, only about 30 seconds after you figured out what to do.
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by bpgen » Thu Apr 01, 2010 8:37 pm
Again it's a combination problem, take total combination of 2 team out of 8 team, i.e 8C2=>8*7/2=>28
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by magicmover » Tue May 24, 2011 5:25 am
What if instead of 2 teams, 3 teams play a game then how do we find total number of games.
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by tomatos » Fri May 25, 2012 7:44 pm
magicmover wrote:What if instead of 2 teams, 3 teams play a game then how do we find total number of games.
8!/(5!)(3!) = 56
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by Brent@GMATPrepNow » Thu Jan 09, 2020 6:35 am
nhai2003 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
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

--------------------------
Here are three related questions:
https://www.beatthegmat.com/ugghhh-i-pi ... 67675.html
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Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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